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eels torun dante nations

eels torun dante nations

An automaton $\bf A$ is called a retractable automaton if, for every subautomaton $\bf B$ of $\bf A$, there is at least one homomorphism of $\bf A$ onto $\bf B$ which leaves the elements of $B$ fixed (such homomorphism is called a retract homomorphism of $\bf A$ onto $\bf B$). We say that a retractable automaton ${\bf A}$=(A,X,$\delta$) is Boolean-type if there exists a family $\{\lambda_B \mid \textrm{ B is a subautomaton of A } \}$ of retract homomorphisms $\lambda _B$ of $\bf A$ such that, for arbitrary subautomata ${\bf B}_1$ and ${\bf B}_2$ of $\bf A$, the condition $B_1\subseteq B_2$ implies $Ker\lambda _{B_2}\subseteq Ker\lambda _{B_1}$. In this paper we describe the Boolean-type retractable state-finite automata without outputs.

An automaton $\bf A$ is called a retractable automaton if, for every subautomaton $\bf B$ of $\bf A$, there is at least one homomorphism of $\bf A$ onto $\bf B$ which leaves the elements of $B$ fixed (such homomorphism is called a retract homomorphism of $\bf A$ onto $\bf B$). We say that a retractable automaton ${\bf A}$=(A,X,$\delta$) is Boolean-type if there exists a family $\{\lambda_B \mid \textrm{ B is a subautomaton of A } \}$ of retract homomorphisms $\lambda _B$ of $\bf A$ such that, for arbitrary subautomata ${\bf B}_1$ and ${\bf B}_2$ of $\bf A$, the condition $B_1\subseteq B_2$ implies $Ker\lambda _{B_2}\subseteq Ker\lambda _{B_1}$. In this paper we describe the Boolean-type retractable state-finite automata without outputs.

An automaton $\bf A$ is called a retractable automaton if, for every subautomaton $\bf B$ of $\bf A$, there is at least one homomorphism of $\bf A$ onto $\bf B$ which leaves the elements of $B$ fixed (such homomorphism is called a retract homomorphism of $\bf A$ onto $\bf B$). We say that a retractable automaton ${\bf A}$=(A,X,$\delta$) is Boolean-type if there exists a family $\{\lambda_B \mid \textrm{ B is a subautomaton of A } \}$ of retract homomorphisms $\lambda _B$ of $\bf A$ such that, for arbitrary subautomata ${\bf B}_1$ and ${\bf B}_2$ of $\bf A$, the condition $B_1\subseteq B_2$ implies $Ker\lambda _{B_2}\subseteq Ker\lambda _{B_1}$. In this paper we describe the Boolean-type retractable state-finite automata without outputs.

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Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type hierarchy upon this interpretation of the base type gives a finite semantics for simply-typed lambda-trees. A calculus based on this semantics is proven sound and complete. In particular, for regular infinite lambda-trees it is decidable whether a given automaton has a run or not. As regular lambda-trees are precisely recursion schemes, this decidability result holds for arbitrary recursion schemes of arbitrary level, without any syntactical restriction.

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various degrees of decomposability between undecomposable and perfectly decomposable are shown to exist.

simulation of finite automata

simulation of finite automata

This study examines various computational techniques to analyze dynamic response and failure of sandwich composite materials subject to fluid-structure interaction characterized by an acoustic field or the propagation of velocity potential according to the wave equation. A displacement-only plate finite element is developed and implemented using Discontinuous Galerkin (DG) methodology; its accuracy compares favorably to both theory and Continuous Galerkin methods. Several approaches to analyzing debonding failure between skin and core layers of sandwich com-posite structures are demonstrated and evaluated; partial disconnection between neighboring elements at a debonding site shows good qualitative agreement with known physical phenomena. A hybrid Finite Element-Cellular Automata (FE+CA) approach to modeling an acoustic field with non-reflecting boundary conditions is presented, validated nu-merically, and favorably compared with experimental results. The FE+CA fluid model is then combined with the DG structural model to simulate fluid-structure interaction; this combined model compared favorably with experimental results for the strain field of laminated plates subject to low-velocity impact. Each technique addressed shows promise for flexible and accurate modeling of failure initiation and propagation in sandwich and laminate composites subject to fluid-structure interaction with moderate computational costs.

The problem addressed in this paper is heuristically-guided learning of finite automata from examples. Given positive sample strings and negative sample strings, a finite automaton is generated and incrementally refined to accept all positive samples but do no negative samples. This paper describes some experiments in applying hill-climbing to modify finite automata to accept a desired regular language. We show that many problems can be solved by this simple method. We then describe the method how to 're-construct' a finite automaton if the positive and/or negative samples are slightly altered, without starting from the beginning. Finally, we have an actual system. RR: Regular set Recognizer, that learns to recognize a regular set from the samples that are given by a human teacher one by one.

Finite state automata are an undeservedly underestimated data structure because most people think they are complex to build. Recent additions to Lucene show that FSAs (and transducers) are very efficient and are applicable to many problems with great results. This talk will introduce FSAs, quickly glance over their construction algorithms and physical automaton representation in Lucene and proceed with practical examples of where FSAs are used with success. Source: https://vimeo.com/26517310 Uploader: newthinking

Finite state automata are an undeservedly underestimated data structure because most people think they are complex to build. Recent additions to Lucene show that FSAs (and transducers) are very efficient and are applicable to many problems with great results. This talk will introduce FSAs, quickly glance over their construction algorithms and physical automaton representation in Lucene and proceed with practical examples of where FSAs are used with success. Source: https://vimeo.com/26517310 Uploader: newthinking

Bell System Technical Journal, 39: 5. September 1960 pp 1267-1295. Automata and Finite Automata. (Lee, C.Y.)

Bell System Technical Journal, 39: 5. September 1960 pp 1267-1295. Automata and Finite Automata. (Lee, C.Y.)

In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Belohlavek [Inform Sciences 143 (2002) 205-209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68-92], Ignjatovi\'c et al. [Inform Sciences 178 (2008) 164-180], and Jan\v{c}i\'c et al. [Inform Sciences 181 (2011) 1358-1368], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jan\v{c}i\'c and \'Ciri\'c [Fuzzy Set Syst (2014), to appear], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performances.

In this paper we combine determinization and state reduction methods into two-in-one algorithms that simultaneously perform determinization and state reduction. These algorithms perform better than all previous determinization algorithms for fuzzy finite automata, developed by Belohlavek [Inform Sciences 143 (2002) 205-209], Li and Pedrycz [Fuzzy Set Syst 156 (2005) 68-92], Ignjatovi\'c et al. [Inform Sciences 178 (2008) 164-180], and Jan\v{c}i\'c et al. [Inform Sciences 181 (2011) 1358-1368], in the sense that they produce smaller automata, while require the same computation time. The only exception is the Brzozowski type determinization algorithm developed recently by Jan\v{c}i\'c and \'Ciri\'c [Fuzzy Set Syst (2014), to appear], which produces a minimal crisp-deterministic fuzzy automaton, but the algorithms created here can also be used within the Brzozowski type algorithm and improve its performances.

It is known that an ordinal is the order type of the lexicographic ordering of a regular language if and only if it is less than omega^omega. We design a polynomial time algorithm that constructs, for each well-ordered regular language L with respect to the lexicographic ordering, given by a deterministic finite automaton, the Cantor Normal Form of its order type. It follows that there is a polynomial time algorithm to decide whether two deterministic finite automata accepting well-ordered regular languages accept isomorphic languages. We also give estimates on the size of the smallest automaton representing an ordinal less than omega^omega, together with an algorithm that translates each such ordinal to an automaton.

There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation property seems to be easy. This paper aims at identifying the reasons why simple proofs break, among them artifacts in the semantics that lead to stuttering steps in the simulation. We then present a semantics based on the zipper data structure, with a direct interpretation of evaluation as navigation in the syntax tree. The abstraction function is then defined by equivalence class construction.

We say that a word $w$ on a totally ordered alphabet avoids the word $v$ if there are no subsequences in $w$ order-equivalent to $v$. In this paper we suggest a new approach to the enumeration of words on at most $k$ letters avoiding a given pattern. By studying an automaton which for fixed $k$ generates the words avoiding a given pattern we derive several previously known results for these kind of problems, as well as many new. In particular, we give a simple proof of the formula \cite{Reg1998} for exact asymptotics for the number of words on $k$ letters of length $n$ that avoids the pattern $12...(\ell+1)$. Moreover, we give the first combinatorial proof of the exact formula \cite{Burstein} for the number of words on $k$ letters of length $n$ avoiding a three letter permutation pattern.

Given a new definition for the entropy of a cellular automata acting on a two-dimensional space, we propose an inequality between the entropy of the shift on a two-dimensional lattice and some angular analog of Lyapunov exponents.

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs is equal to the power of 1-way reversible automata. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. Namely, we construct a 1-way QFA which is exponentially smaller than any equivalent classical (even randomized) finite automaton. This construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.

Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we identify the key properties used to interpret automata and propose a modification of a state-merging approach to learn variants of finite state automata. We apply the approach to problems beyond typical grammar inference tasks. Additionally, we cover several use-cases for prediction, classification, and clustering on sequential data in both supervised and unsupervised scenarios to show how the identified key properties are applicable in a wide range of contexts.

The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic sequences includes the class of eventually strongly almost periodic sequences, and we prove this inclusion to be strict. We prove that the class of eventually strongly almost periodic sequences is closed under finite automata mappings and finite transducers. Moreover, an effective form of this result is presented. Finally we consider some algorithmic questions concerning almost periodicity.

Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA and propose a new computing model called {\it two-way two-tape finite automata with quantum and classical states} (2TQCFA). First, we give efficient 2TFA algorithms for recognizing languages which can be recognized by 2QCFA. Second, we give efficient 2TQCFA algorithms to recognize several languages whose status vis-a-vis 2QCFA have been posed as open questions, such as $L_{square}=\{a^{n}b^{n^{2}}\mid n\in \mathbf{N}\}$. Third, we show that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by {\it $(k+1)$-tape deterministic finite automata} ($(k+1)$TFA). Finally, we introduce {\it $k$-tape automata with quantum and classical states} ($k$TQCFA) and prove that $\{a^{n}b^{n^{k}}\mid n\in \mathbf{N}\}$ can be recognized by $k$TQCFA.

Using a novel rewriting problem, we show that several natural decision problems about finite automata are undecidable (i.e., recursively unsolvable). In contrast, we also prove three related problems are decidable. We apply one result to prove the undecidability of a related problem about k-automatic sets of rational numbers.

We examine the NFA minimization problem in terms of atomic NFA's, that is, NFA's in which the right language of every state is a union of atoms, where the atoms of a regular language are non-empty intersections of complemented and uncomplemented left quotients of the language. We characterize all reduced atomic NFA's of a given language, that is, those NFA's that have no equivalent states. Using atomic NFA's, we formalize Sengoku's approach to NFA minimization and prove that his method fails to find all minimal NFA's. We also formulate the Kameda-Weiner NFA minimization in terms of quotients and atoms.

We examine the NFA minimization problem in terms of atomic NFA's, that is, NFA's in which the right language of every state is a union of atoms, where the atoms of a regular language are non-empty intersections of complemented and uncomplemented left quotients of the language. We characterize all reduced atomic NFA's of a given language, that is, those NFA's that have no equivalent states. Using atomic NFA's, we formalize Sengoku's approach to NFA minimization and prove that his method fails to find all minimal NFA's. We also formulate the Kameda-Weiner NFA minimization in terms of quotients and atoms.

In this note, we generalize the results of arXiv:0901.2703v1 We show that all one-way quantum finite automaton (QFA) models that are at least as general as Kondacs-Watrous QFA's are equivalent in power to classical probabilistic finite automata in this setting. Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input does enlarge the class of languages recognized by such QFA's with unbounded error. (Note that, the proof of Theorem 1 in the abstract was presented in the previous version (arXiv:0901.2703v1).)

In this note, we generalize the results of arXiv:0901.2703v1 We show that all one-way quantum finite automaton (QFA) models that are at least as general as Kondacs-Watrous QFA's are equivalent in power to classical probabilistic finite automata in this setting. Unlike their probabilistic counterparts, allowing the tape head to stay put for some steps during its traversal of the input does enlarge the class of languages recognized by such QFA's with unbounded error. (Note that, the proof of Theorem 1 in the abstract was presented in the previous version (arXiv:0901.2703v1).)

We investigate the condition under which the Eulerian trail of a digraph is unique, and design a finite automaton to examine it. The algorithm is effective, for if the condition is violated, it will be noticed immediately without the need to trace through the whole trail.

In automata theory a minimization is the task of transforming a given finite state machine into an equivalent automation that has a minimum number of states. Here, the reduction of Deterministic Finite Automata(DFA) is very simple whereas Nondeterministic Finite Automata(NFA) is complex because which has maximium number of possible paths to reach new states. So a minimal NFA is a primal problem in automata theory. We consider the problem of approximating a minimal NFA or a minimal regular expression. There are several approaches to NFA minimization either without approximation guarantees or running in at least exponential time. Here this paper introducing the new NFA reduction algorithm for the minimization of NFA. This algorithm will reduce number of state transitions of Nondeterministic Finite Automata. NFA reduction algorithm also resolves the complexity of Kameda- Weiner algorithm. This paper shown empirically that this algorithm is effective in largely reducing the memory requirement of NFA minimization algorithm. Reducing the size of NFA by using NFA Reduction Algorithm has been shown to reduce importantly the search time. G. Mutyalamma | K. Komali | G. Pushpa"A Novel Algorithm for Reduction of Non-Deterministic Finite Automata" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd8233.pdf Article URL: http://www.ijtsrd.com/computer-science/other/8233/a-novel-algorithm-for-reduction-of--non-deterministic-finite-automata/g-mutyalamma

Let $X=S^G$ where $G$ is a countable group and $S$ is a finite set. A cellular automaton (CA) is an endomorphism $T : X \to X$ (continuous, commuting with the action of $G$). Shereshevsky (1993) proved that for $G=Z^d$ with $d>1$ no CA can be forward expansive, raising the following conjecture: For $G=Z^d$, $d>1$ the topological entropy of any CA is either zero or infinite. Morris and Ward (1998), proved this for linear CA's, leaving the original conjecture open. We show that this conjecture is false, proving that for any $d$ there exist a $d$-dimensional CA with finite, nonzero topological entropy. We also discuss a measure-theoretic counterpart of this question for measure-preserving CA's. Our main tool is a construction of a CA by Kari (1994).

Let $X=S^G$ where $G$ is a countable group and $S$ is a finite set. A cellular automaton (CA) is an endomorphism $T : X \to X$ (continuous, commuting with the action of $G$). Shereshevsky (1993) proved that for $G=Z^d$ with $d>1$ no CA can be forward expansive, raising the following conjecture: For $G=Z^d$, $d>1$ the topological entropy of any CA is either zero or infinite. Morris and Ward (1998), proved this for linear CA's, leaving the original conjecture open. We show that this conjecture is false, proving that for any $d$ there exist a $d$-dimensional CA with finite, nonzero topological entropy. We also discuss a measure-theoretic counterpart of this question for measure-preserving CA's. Our main tool is a construction of a CA by Kari (1994).

The nondeterministic quantum finite automaton (NQFA) is the only known case where a one-way quantum finite automaton (QFA) model has been shown to be strictly superior in terms of language recognition power to its probabilistic counterpart. We give a characterization of the class of languages recognized by NQFA's, demonstrating that it is equal to the class of exclusive stochastic languages. We also characterize the class of languages that are recognized necessarily by two-sided error by QFA's. It is shown that these classes remain the same when the QFA's used in their definitions are replaced by several different model variants that have appeared in the literature. We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.

The paper proposed an algorithm which purpose is searching for a substring of characters in a string. Principle of its operation is based on the theory of non-deterministic finite automata and vector-character architecture. It is able to provide the linear computational complexity of searching for a substring depending on the length of the searched string measured in the number of operations with hyperdimensional vectors when repeatedly searching for different strings in a target line. None of the existing algorithms has such a low level of computational complexity. The disadvantages of the proposed algorithm are the fact that the existing hardware implementations of computing systems for performing operations with hyperdimensional vectors require a large number of machine instructions, which reduces the gain from this algorithm. Despite this, in the future, it is possible to create a hardware implementation that can ensure the execution of operations with hyperdimensional vectors in one cycle, which will allow the proposed algorithm to be applied in practice.

Let $x$ be an $m$-sequence, a maximal length sequence produced by a linear feedback shift register. We show that the nondeterministic automatic complexity $A_N(x)$ is close to maximal: $n/2-A_N(x)=O(\log^2n)$, whereas Hyde has shown $A_N(y)\le n/2+1$ for all sequences $y$.

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.

This article studies the expressive power of finite automata recognizing sets of real numbers encoded in positional notation. We consider Muller automata as well as the restricted class of weak deterministic automata, used as symbolic set representations in actual applications. In previous work, it has been established that the sets of numbers that are recognizable by weak deterministic automata in two bases that do not share the same set of prime factors are exactly those that are definable in the first order additive theory of real and integer numbers. This result extends Cobham's theorem, which characterizes the sets of integer numbers that are recognizable by finite automata in multiple bases. In this article, we first generalize this result to multiplicatively independent bases, which brings it closer to the original statement of Cobham's theorem. Then, we study the sets of reals recognizable by Muller automata in two bases. We show with a counterexample that, in this setting, Cobham's theorem does not generalize to multiplicatively independent bases. Finally, we prove that the sets of reals that are recognizable by Muller automata in two bases that do not share the same set of prime factors are exactly those definable in the first order additive theory of real and integer numbers. These sets are thus also recognizable by weak deterministic automata. This result leads to a precise characterization of the sets of real numbers that are recognizable in multiple bases, and provides a theoretical justification to the use of weak automata as symbolic representations of sets.

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eksperyment turinga bacha roboty

eksperyment turinga bacha roboty

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests.

We study alternating register automata on data words and data trees in relation to logics. A data word (resp. data tree) is a word (resp. tree) whose every position carries a label from a finite alphabet and a data value from an infinite domain. We investigate one-way automata with alternating control over data words or trees, with one register for storing data and comparing them for equality. This is a continuation of the study started by Demri, Lazic and Jurdzinski. From the standpoint of register automata models, this work aims at two objectives: (1) simplifying the existent decidability proofs for the emptiness problem for alternating register automata; and (2) exhibiting decidable extensions for these models. From the logical perspective, we show that (a) in the case of data words, satisfiability of LTL with one register and quantification over data values is decidable; and (b) the satisfiability problem for the so-called forward fragment of XPath on XML documents is decidable, even in the presence of DTDs and even of key constraints. The decidability is obtained through a reduction to the automata model introduced. This fragment contains the child, descendant, next-sibling and following-sibling axes, as well as data equality and inequality tests.

We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with the model of L\={a}ce et al. We examine the related language classes, and also establish separations between the classical and quantum versions, and between the zero-error vs. bounded-error modes of recognition in this model.

This paper deals with the size complexity of minimal {\it two-way quantum finite automata} (2qfa's) necessary for operations to perform on all inputs of each fixed length. Such a complexity measure, known as state complexity of operations, is useful in measuring how much information is necessary to convert languages. We focus on intersection, union, reversals, and catenation operations and show some upper bounds of state complexity of operations on 2qfa's. Also, we present a number of non-regular languages and prove that these languages can be accepted by 2qfa's with one-sided error probabilities within linear time. Notably, these examples show that our bounds obtained for these operations are not tight, and therefore worth improving. We give an instance to show that the upper bound of the state number for the simulation of one-way deterministic finite automata by two-way reversible finite automata is not tight in general.

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state automata with a specified number, $m$, of states to the set of all binary sequences. Thus we can index the complexity of our random sequence by the number of states of the automata. We detail optimal algorithms to predict sequences generated in this way.

Multi-letter {\it quantum finite automata} (QFAs) were a new one-way QFA model proposed recently by Belovs, Rosmanis, and Smotrovs (LNCS, Vol. 4588, Springer, Berlin, 2007, pp. 60-71), and they showed that multi-letter QFAs can accept with no error some regular languages ($(a+b)^{*}b$) that are unacceptable by the one-way QFAs. In this paper, we continue to study multi-letter QFAs. We mainly focus on two issues: (1) we show that $(k+1)$-letter QFAs are computationally more powerful than $k$-letter QFAs, that is, $(k+1)$-letter QFAs can accept some regular languages that are unacceptable by any $k$-letter QFA. A comparison with the one-way QFAs is made by some examples; (2) we prove that a $k_{1}$-letter QFA ${\cal A}_1$ and another $k_{2}$-letter QFA ${\cal A}_2$ are equivalent if and only if they are $(n_{1}+n_{2})^{4}+k-1$-equivalent, and the time complexity of determining the equivalence of two multi-letter QFAs using this method is $O(n^{12}+k^{2}n^{4}+kn^{8})$, where $n_{1}$ and $n_{2}$ are the numbers of states of ${\cal A}_{1}$ and ${\cal A}_{2}$, respectively, and $k=\max(k_{1},k_{2})$. Some other issues are addressed for further consideration.

1Born Again

By Alfred Lawson

"I doubt that anyone who reads [Born Again] will ever forget it: it is quite singularly bad, with long indigestible rants against the evils of the world, an impossibly idealistic Utopian prescription for the said evils, and - as you will have gathered - a very silly plot." - oddbooks.co.uk<br /><br /> Alfred Lawson was a veritable Renaissance man: a professional baseball player, a luminary in the field of aviation, an outspoken advocate of vegetarianism and economic reform, and the founder of a pseudo-scientific crackpot philosophy called Lawsonomy. Born Again, his only novel, is a bizarre, delirious, and delightfully silly utopian science-fiction novel that lays the groundwork for the philosophy that would later dominate Lawson's life. It tells the story of John Convert, a wayward, seafaring soul (based loosely on Lawson, minus the conveniently symbolic initials) who is tossed overboard by his crewmen after a physical altercation. Convert awakens on an island inhabited by a race of superhuman giants -- called the Sagemen -- who slumber in their subterranean city. He then meets Arletta, a giantess who takes Convert on a journey that will change his life in ways too fantastically strange to imagine. (Introduction by ChuckW)

A beautiful collection of pretty little poems. (Summary by Charlotte Duckett)

In 1892, two of Australia's best poets came up with a scheme to make some money. They arranged to have an argument in the Weekly Bulletin, and since they were being paid by the word, this let them fire back and forth, being sent beer money with each salvo. A couple of other poets also joined in, and their work is seminal to the development of the Bush ethos in Australia.<br /><br /> The first eight files are the original form of the poems, and the second eight are later republications by the authors, in their own collections. (Summary by Timothy Ferguson)

Henry Lawson was an Australian writer and poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". (Summary by Wikipedia)

5Shame of Going Back

By Henry Lawson

Henry Archibald Hertzberg Lawson was an Australian writer and poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". - Summary by Wikipedia

6Men Who Live It Down

By Henry Lawson

MANY of the verses in this volume (When I Was King (1906)) appeared originally in the SYDNEY Bulletin, others in the Daily Telegraph, Town and Country Journal, Evening News, World's News, Australian Star, Amateur Gardener, and KALGOORLIE Sun, while eleven are reprinted from The Children of the Bush, published by Messrs. Methuen and Co., London. (from the Introduction)

7In the Days When the World Was Wide, and Other Verses

By Henry Lawson

This is a volume of poetry by Henry Lawson, the well-known Australian poet. Some of the poems in this collection are still widely taught in school, some others are not widely known at this time. All of them, however, paint vivid images of Australia around the turn of the last century. As <i>The Academy</i> put it in 1909, "These ballads (for such they mostly are) abound in spirit and manhood, in the colour and smell of Australian soil. They deserve the popularity which they have won in Australia, and which, we trust, this edition will now give them in England." - Summary by Carolin

Henry Archibald Hertzberg Lawson was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". He was the son of the poet, publisher and feminist Louisa Lawson. - Summary by Wikipedia

This poem tells the story of a boy in Australia who leaves the farm at harvest time. "and to run from home was a crime." The story is set in the Riverina, New South Wales in the town of Gundagai. ( David Lawrence)

10Shakedown on the Floor

By Henry Lawson

Despite the bittersweet outcome of the romance in this work, the poem still manages to conclude in an uplifting fashion. - Summary by SonOfTheExiles

11Verses Popular And Humorous (Version 2)

By Henry Lawson

Verses, Popular and Humorous (1900) was the second collection of poems by Australian poet Henry Lawson. It features some of the poet's earlier major works, including "The Lights of Cobb and Co", "Saint Peter" and "The Grog-An'-Grumble-Steeplechase". Most of the poems in the volume had been written after the publication of In the Days When the World was Wide and Other Verses in 1896.<br /> The original collection includes 66 poems by the author that are reprinted from various sources. Later publications split the collection into two separate volumes: Popular Verses and Humorous Verses, though the contents differed from the original list. - Summary by Wikipedia <br /><br /> Initial DPL: Larry Wilson and MC: Phil Chenevert

12Verses Popular and Humorous

By Henry Lawson

This is a volume of humorous poems by Australian poet Henry Lawson. - Summary by Carolin

13Outside Track

By Henry Lawson

LibriVox volunteers bring you 9 recordings of The Outside Track by Henry Lawson.<br> his was the Fortnightly Poetry project for August 25, 2019. <br> ------<br> Henry Archibald Hertzberg Lawson was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". - Summary by Wikipedia

01. That Pretty Girl in the Army<br><br>The Salvation Army is having a hard time of things in the rough Outback town of Bourke.  That is, until Sister Hannah arrives... - Summary by Son of the Exiles <BR><BR>Coordinated by: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Sister Hannah: <a href="https://librivox.org/reader/11084">Devorah Allen</a><br> Jack Moonlight: <a href="https://librivox.org/reader/10789">Tomas Peter</a><br> Billy Woods: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> Jake Boreham: <a href="https://librivox.org/reader/8425">Larry Wilson</a><br> Reformed Drunkard: <a href="https://librivox.org/reader/12980">Wayne Cooke</a><br> Bob Brothers: <a href="https://librivox.org/reader/4705">Algy Pug</a><br> Mitchell: <a href="https://librivox.org/reader/7170">Alan Mapstone</a><br> Donald Macdonald: <a href="https://librivox.org/reader/7026">Michele Eaton</a><br> One-Eyed Bogan: <a href="https://librivox.org/reader/11927">lorda</a><br> Female Testifier: <a href="https://librivox.org/reader/11059">Lauren-Emma Blake</a><br> Blunderer: <a href="https://librivox.org/reader/16484">Therese Lindholm</a><br> Black Testifier: <a href="https://librivox.org/reader/12980">Wayne Cooke</a><br> Heckler: <a href="https://librivox.org/reader/6754">ToddHW</a><br> Narrator: <a href="https://librivox.org/reader/8677">KHand</a><br><BR> 02. The Hairy Man<br><br>It was the day after Australia's Anniversary Day and all the patriots wanted to do was nurse their hangovers out in the scrub of the isolated western spur of the Blue Mountains. But following close on the heels of their hair-of-the-dog comes The Hairy Man, Australia's own version of Bigfoot. - Summary by Son of the Exiles<br><br>Coordinated by: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Jack Jones: <a href="https://librivox.org/reader/7170">Alan Mapstone</a><br> Andy Page: <a href="https://librivox.org/reader/8425">Larry Wilson</a><br> Dave Regan: <a href="https://librivox.org/reader/11927">lorda</a><br> Jim Bentley: <a href="https://librivox.org/reader/6754">ToddHW</a><br> Mahoney: <a href="https://librivox.org/reader/11790">TJ Burns</a><br> Foley: <a href="https://librivox.org/reader/4705">Algy Pug</a><br> Narrator: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br><BR> 03. Macquarie's Mate<br><br>Even "the veriest wreck in the drink-fiend's clutch" won't stand idly by and hear his mate slagged off. - Summary by Son of the Exiles <br><br>Coordinated by: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Awful Example: <a href="https://librivox.org/reader/7170">Alan Mapstone</a><br> Box-o’-Tricks: <a href="https://librivox.org/reader/6754">ToddHW</a><br> Barcoo: <a href="https://librivox.org/reader/4705">Algy Pug</a><br> “Sally” Thompson: <a href="https://librivox.org/reader/7026">Michele Eaton</a><br> Stiffner the Shanty-Keeper: <a href="https://librivox.org/reader/10995">April6090</a><br> Macquarie: <a href="https://librivox.org/reader/11927">lorda</a><br> Somebody: <a href="https://librivox.org/reader/14540">Andrew Gaunce</a><br> Narrator: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br><BR> 04. His Country After All<br><br>"Lives there a man with soul so dead..." - Summary taken from text<br><br>Coordinated by: <a href="https://librivox.org/reader/8879">Son of the Exiles</a><br> Australian-born American: <a href="https://librivox.org/reader/12980">Wayne Cooke</a><br> New Zealand bagman: <a href="https://librivox.org/reader/10801">Jim Locke</a><br> Coach Driver: <a href="https://librivox.org/reader/6754">ToddHW</a><br> Posh-sounding British voice: <a href="https://librivox.org/reader/7170">Alan Mapstone</a><br> Australian rabbit-trapper: <a href="https://librivox.org/reader/4705">Algy Pug</a><br> Narrator: <a href="https://librivox.org/reader/8677">KHand</a><br>

15Ship

By Henry Lawson

LibriVox volunteers bring you 11 recordings of The Ship by Henry Lawson.<br> This was the Fortnightly Poetry project for November 1, 2020. <br> ------<br> Remembrance Day 2020; An excerpt from A Fantasy of War in the book My Army, O, My Army! and other songs by Henry Lawson (1915) - Summary by David Lawrence

16Route March

By Henry Lawson

LibriVox volunteers bring you 16 recordings of The Route March by Henry Lawson.<br> This was the Weekly Poetry project for November 8, Remembrance Day 2020.

17Above Lavender Bay

By Henry Lawson

LibriVox volunteers bring you 14 recordings of Above Lavender Bay by Henry Lawson.<br> This was the Fortnightly Poetry project for January 10, 2021. <br> ------<br> Henry Archibald Hertzberg Lawson was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". This poem is taken from The Skyline Riders and Other Verses By Henry Lawson (1910) - Summary by Wikipedia

18Selected Lead Articles from "THE DAWN"

By Louisa Lawson

Louisa Lawson, the mother of Australian writer Henry Lawson, was the founder, publisher and editor of an early feminist journal in Sydney named “The Dawn”. From 1888 onwards, it played no small part in the gaining of the vote for Australian women in South Australia (1895), Western Australia (1899), New South Wales (1902), Commonwealth (1902), Tasmania (1903), Queensland (1905), and Victoria (1908). <br><br> Since the success of the “Digitise The Dawn” project, a number of Louisa Lawson’s lead articles from the journal are available PD online, including the one written in defiance of the male-dominated New South Wales Typographical Association. This union attempted to shut down The Dawn by getting up an advertising boycott and other methods, angered as they were by The Dawn’s all-woman team of editors and printers … the NSW Typographical Association objected to them employing women at all. <br><br> Louisa Lawson described one attempt at intimidation to the 'Bulletin' : <br></br> <i>'We were just going to press, and you know how locking up isn't always an easy matter-particularly for new chums like we were. Well he stood there and said nasty things, and poor Miss Grieg-she's my forewoman-and the girls, they got as white as chalk; the tears were in their eyes. I asked him three times to go, and he wouldn't, so I took a watering pot full of water that we had for sweeping the floor, and I let him have it.'</i> <br><br> The advertising boycott in time collapsed after Louisa Lawson suggested her readers adopt the following simple expedient:<br><br> <i>‘If it is made clear to your tradesmen that you deal with them because they advertise with us, the boycott is immediately defeated.’</i> <br><br>- Summary by Son of the Exiles

19Reedy River

By Henry Lawson

LibriVox volunteers bring you 12 recordings of Reedy River by Henry Lawson..<br> This was the Fortnightly Poetry project for August 22, 2021. <br> ------<br> This Fortnightly Poem is taken from Verses Popular and Humorous (pub 1900). This was the second collection of poems by Australian poet Henry Lawson. - Summary by David Lawrence

20Short Stories in Prose and Verse

By Henry Lawson

Short Stories in Prose and Verse” is Henry Lawson’s first published book (1894); his first published poem appeared in 1887. The volume is a snapshot of his writing style up to the start of his career. His first published poem appeared at age 20, his first published book at age 27. This volume is a good sample of Henry Lawson’s poetry and prose and makes a good stepping-stone towards the enjoyment of his later works. Summary by Chris Greaves

"A collection of the important and interesting criminal trials which have taken place in the United States from the beginning of our government to the present day".<br><br> To the general public this series will certainly appeal as the most interesting and instructive work which has been published in this country for many years. The trial of judicial causes has even more charms than biography and history, for it is a drama of real life. We enter the halls of justice, the judges and jurors are before us, the criminal is brought in, we behold him surrounded by an eager and excited populace; the whole scene passing before the mind's eye as a living and moving picture. There is nothing in the Grecian drama that surpasses, in touching pathos, scenes in the trials and prosecutions of these men and women, sometimes innocent and sometimes guilty, but always awaiting with trembling the verdict of the jury which is to send them back to their families and friends or to the scaffold or prison. Here are the poor and ignorant confronted with their accusers but relying upon their advocates; there the rich and powerful surrounded by a host of counsel and braving even the power of the government to convict them. Sometimes the mere report of the evidence in the case and the verdict gives a complete picture of the crime and criminal but in most cases the full dramatic effect cannot be shown in a narrative, but stands out broadly and as vividly as the actual trial when the witnesses, the counsel, the judge and the prisoner are suffered to speak for themselves. in many cases the great points of interest are the eloquent arguments at the bar by the advocates, and in this collection will be included all the great forensic efforts which have been made in trials in all the States by the orators and leaders of the American Bar from the beginning of American Courts down to the present time. When it is considered how prone our people are to litigation, what a vast number of causes are decided every year, how eagerly the public attention is directed to many of them, what an amount of learning and talent are centered in the legal profession, greater perhaps than in any other, how fond American people are of attending courts, and especially the magnitude of many causes that are tried, it is extraordinary that there should not have appeared up to this time in the country a series of American State Trials. - Summary from the Introduction

22Pet Reader

By Edith W. Lawson

Little rhymes and bits of verse about animals to entertain and instruct primary children. - Summary by TR Love

23Pride That Comes After

By Henry Lawson

LibriVox volunteers bring you 18 recordings of The Pride That Comes After By Henry Lawson.<br> This was the Weekly Poetry project for May 28, 2023. <br> ------<br> Henry Archibald Hertzberg Lawson was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". - Summary by Wikipedia

"A collection of the important and interesting criminal trials which have taken place in the United States from the beginning of our government to the present day". To the general public this series will certainly appeal as the most interesting and instructive work which has been published in this country for many years. The trial of judicial causes has even more charms than biography and history, for it is a drama of real life. We enter the halls of justice, the judges and jurors are before us, the criminal is brought in, we behold him surrounded by an eager and excited populace; the whole scene passing before the mind's eye as a living and moving picture. There is nothing in the Grecian drama that surpasses, in touching pathos, scenes in the trials and prosecutions of these men and women, sometimes innocent and sometimes guilty, but always awaiting with trembling the verdict of the jury which is to send them back to their families and friends or to the scaffold or prison. Here are the poor and ignorant confronted with their accusers but relying upon their advocates; there the rich and powerful surrounded by a host of counsel and braving even the power of the government to convict them. Sometimes the mere report of the evidence in the case and the verdict gives a complete picture of the crime and criminal but in most cases the full dramatic effect cannot be shown in a narrative, but stands out broadly and as vividly as the actual trial when the witnesses, the counsel, the judge and the prisoner are suffered to speak for themselves. in many cases the great points of interest are the eloquent arguments at the bar by the advocates, and in this collection will be included all the great forensic efforts which have been made in trials in all the States by the orators and leaders of the American Bar from the beginning of American Courts down to the present time. When it is considered how prone our people are to litigation, what a vast number of causes are decided every year, how eagerly the public attention is directed to many of them, what an amount of learning and talent are centered in the legal profession, greater perhaps than in any other, how fond American people are of attending courts, and especially the magnitude of many causes that are tried, it is extraordinary that there should not have appeared up to this time in the country a series of American State Trials. - Summary by Introduction

J. GIlchrist Lawson was an American Baptist evangelist and prohibitionist who was also active as an author and editor. This book has been of enduring value and influence as who delves into the deeper, inner spirituality of notable Christians of historical influence. His primary focus is on the experience of the baptism, or infilling, of the Holy Spirit, or entire sanctification, and how this transformed the character and activity of these Christians. After drawing from characters of the Old and New Testaments and the early saints of the church, Lawson gives penetrating portraits of such figures as John Wesley, George Whitefield, George Fox, Madam Guyon, Charles Finney, D.L. Moody, William Booth, and many others. - Summary by Larry Wilson

"A collection of the important and interesting criminal trials which have taken place in the United States from the beginning of our government to the present day". To the general public this series will certainly appeal as the most interesting and instructive work which has been published in this country for many years. The trial of judicial causes has even more charms than biography and history, for it is a drama of real life. We enter the halls of justice, the judges and jurors are before us, the criminal is brought in, we behold him surrounded by an eager and excited populace; the whole scene passing before the mind's eye as a living and moving picture. There is nothing in the Grecian drama that surpasses, in touching pathos, scenes in the trials and prosecutions of these men and women, sometimes innocent and sometimes guilty, but always awaiting with trembling the verdict of the jury which is to send them back to their families and friends or to the scaffold or prison. Here are the poor and ignorant confronted with their accusers but relying upon their advocates; there the rich and powerful surrounded by a host of counsel and braving even the power of the government to convict them. Sometimes the mere report of the evidence in the case and the verdict gives a complete picture of the crime and criminal but in most cases the full dramatic effect cannot be shown in a narrative, but stands out broadly and as vividly as the actual trial when the witnesses, the counsel, the judge and the prisoner are suffered to speak for themselves. in many cases the great points of interest are the eloquent arguments at the bar by the advocates, and in this collection will be included all the great forensic efforts which have been made in trials in all the States by the orators and leaders of the American Bar from the beginning of American Courts down to the present time. When it is considered how prone our people are to litigation, what a vast number of causes are decided every year, how eagerly the public attention is directed to many of them, what an amount of learning and talent are centered in the legal profession, greater perhaps than in any other, how fond American people are of attending courts, and especially the magnitude of many causes that are tried, it is extraordinary that there should not have appeared up to this time in the country a series of American State Trials. - Summary by Introduction

"A collection of the important and interesting criminal trials which have taken place in the United States from the beginning of our government to the present day". To the general public this series will certainly appeal as the most interesting and instructive work which has been published in this country for many years. The trial of judicial causes has even more charms than biography and history, for it is a drama of real life. We enter the halls of justice, the judges and jurors are before us, the criminal is brought in, we behold him surrounded by an eager and excited populace; the whole scene passing before the mind's eye as a living and moving picture. There is nothing in the Grecian drama that surpasses, in touching pathos, scenes in the trials and prosecutions of these men and women, sometimes innocent and sometimes guilty, but always awaiting with trembling the verdict of the jury which is to send them back to their families and friends or to the scaffold or prison. Here are the poor and ignorant confronted with their accusers but relying upon their advocates; there the rich and powerful surrounded by a host of counsel and braving even the power of the government to convict them. Sometimes the mere report of the evidence in the case and the verdict gives a complete picture of the crime and criminal but in most cases the full dramatic effect cannot be shown in a narrative, but stands out broadly and as vividly as the actual trial when the witnesses, the counsel, the judge and the prisoner are suffered to speak for themselves. in many cases the great points of interest are the eloquent arguments at the bar by the advocates, and in this collection will be included all the great forensic efforts which have been made in trials in all the States by the orators and leaders of the American Bar from the beginning of American Courts down to the present time. When it is considered how prone our people are to litigation, what a vast number of causes are decided every year, how eagerly the public attention is directed to many of them, what an amount of learning and talent are centered in the legal profession, greater perhaps than in any other, how fond American people are of attending courts, and especially the magnitude of many causes that are tried, it is extraordinary that there should not have appeared up to this time in the country a series of American State Trials. - Summary by Introduction

LibriVox volunteers bring you 18 recordings of Stand by the Engines by Henry Lawson.<br> This was the Fortnightly Poetry project for September 15, 2024. <br> ------<br> Henry Archibald Hertzberg Lawson was an Australian writer and bush poet. Along with his contemporary Banjo Paterson, Lawson is among the best-known Australian poets and fiction writers of the colonial period and is often called Australia's "greatest short story writer". - Summary by Wikipedia

"A collection of the important and interesting criminal trials which have taken place in the United States from the beginning of our government to the present day". To the general public this series will certainly appeal as the most interesting and instructive work which has been published in this country for many years. The trial of judicial causes has even more charms than biography and history, for it is a drama of real life. We enter the halls of justice, the judges and jurors are before us, the criminal is brought in, we behold him surrounded by an eager and excited populace; the whole scene passing before the mind's eye as a living and moving picture. There is nothing in the Grecian drama that surpasses, in touching pathos, scenes in the trials and prosecutions of these men and women, sometimes innocent and sometimes guilty, but always awaiting with trembling the verdict of the jury which is to send them back to their families and friends or to the scaffold or prison. Here are the poor and ignorant confronted with their accusers but relying upon their advocates; there the rich and powerful surrounded by a host of counsel and braving even the power of the government to convict them. Sometimes the mere report of the evidence in the case and the verdict gives a complete picture of the crime and criminal but in most cases the full dramatic effect cannot be shown in a narrative, but stands out broadly and as vividly as the actual trial when the witnesses, the counsel, the judge and the prisoner are suffered to speak for themselves. in many cases the great points of interest are the eloquent arguments at the bar by the advocates, and in this collection will be included all the great forensic efforts which have been made in trials in all the States by the orators and leaders of the American Bar from the beginning of American Courts down to the present time. When it is considered how prone our people are to litigation, what a vast number of causes are decided every year, how eagerly the public attention is directed to many of them, what an amount of learning and talent are centered in the legal profession, greater perhaps than in any other, how fond American people are of attending courts, and especially the magnitude of many causes that are tried, it is extraordinary that there should not have appeared up to this time in the country a series of American State Trials." - Summary by Introduction