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The idea of information encoding on quantum bearers and its quantum-mechanical processing has revolutionized our world and brought mankind on the verge of enigmatic era of quantum technologies. Inspired by this idea, in present paper we search for advantages of quantum information processing in the field of machine learning. Exploiting only basic properties of the Hilbert space, superposition principle of quantum mechanics and quantum measurements, we construct a quantum analog for Rosenblatt's perceptron, which is the simplest learning machine. We demonstrate that the quantum perceptron superiors its classical counterpart in learning capabilities. In particular, we show that the quantum perceptron is able to learn an arbitrary (Boolean) logical function, perform the classification on previously unseen classes and even recognize the superpositions of learned classes -- the task of high importance in applied medical engineering.

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.

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments.

The bandwidth utilization of a single channel-based wireless networks decreases due to congestion and interference from other sources and therefore transmission on multiple channels are needed. In this paper, we propose a distributed dynamic channel allocation scheme for wireless networks using adaptive learning automata whose nodes are equipped with single radio interfaces so that a more suitable channel can be selected. The proposed scheme, Adaptive Pursuit Reward-Inaction, runs periodically on the nodes, and adaptively finds the suitable channel allocation in order to attain a desired performance. A novel performance index, which takes into account the throughput and the energy consumption, is considered. The proposed scheme is adaptive in the sense that probabilities in the each step are updated as a function of the error in the performance index. The extensive simulation results in static and mobile environments provide that using the proposed scheme for channel allocation in the multiple channel wireless networks significantly improves the throughput, drop rate, energy consumption per packet and fairness index.

Consider a repeated two-person game. The question is how much smarter a player must be in order to effectively predict the moves of the other player. The answer depends on the formal definition of effective prediction, the number of actions each player has in the stage game, as well as on the measure of smartness. Effective prediction means that, no matter what the stage-game payoff function, the player can play (with high probability) a best reply in most stages. Neyman and Spencer [4] provide a complete asymptotic solution when smartness is measured by the size of the automata that implement the strategies: Let G = hI, J, gi be a two-person zero-sum game; I and J are the set of actions of player 1 and player 2 respectively, and g : I × J ! R is the payoff function to player 1. Consider the repeated two-person zero-sum game G(k,m) where player 1’s possible strategies are those implementable by an automaton with k states and player 2’s possible strategies are those implementable by an automaton with m states. We say that player 2 can effectively predict the moves of player 1 if for every reaction function r : I ! J player 2 has a strategy (in G(k,m)) such that for every strategy of player 1 the expected empirical distribution of the action pairs (i, j) is essentially supported on the set of action pairs of the form (i, r(i)). [4] characterizes. ©2007 Microsoft Corporation. All rights reserved.

Neural networks are trained to learn their expected behavior. Networks that are designed to learn a particular informational scheme are called learning critical to the operational performance of learning automata. In general, the automata is in some way rewarded for proper behavior and 'punished' for wrong behavior. Initially, all choices of behavior are random, but by using these learning rules of reward and punishment that is used can significantly affect both local and global learning and results in surprising revelations about achieving proper behavior. Learning automata can be applied to a variety of computational problems. For example, a neural network can be trained to recognize which of several available filters, classifiers, or other neural networks are best suited to a particular task. Scientists at the Naval Oceanographic and Atmospheric Research Laboratory's (NOARL's) Map Data Formatting Facility (MDFF) plan to apply this type of neural network training the their research in the automated feature extraction of digital maps. NOARL's dataset of interest consists of scanned aeronautical charts, provided by the Defense Mapping Agency, which are compressed by the MDFF computers into a form that is compatible with digital moving map systems onboard naval aircraft. In an effort to improve the quality of the output images, MDFF computer scientists are testing various digital image enhancement algorithms on this particular dataset. Learning automata could be used to help choose the best digital feature extraction process for a given subtask. For example, the vectorization of desert data requires a significantly different approach that used to classify rugged terrain.

In this paper, we propose a novel algorithm to learn a B\"uchi automaton from a teacher who knows an $\omega$-regular language. The algorithm is based on learning a formalism named family of DFAs (FDFAs) recently proposed by Angluin and Fisman[10]. The main catch is that we use a classification tree structure instead of the standard observation table structure. The worst case storage space required by our algorithm is quadratically better than the table-based algorithm proposed in [10]. We implement the first publicly available library ROLL (Regular Omega Language Learning ), which consists of all $\omega$-regular learning algorithms available in the literature and the new algorithms proposed in this paper. Experimental results show that our tree-based algorithms have the best performance among others regarding the number of solved learning tasks.

Systems, methods and apparatus are provided through which in some embodiments, automata learning algorithms and techniques are implemented to generate a more complete set of scenarios for requirements based programming. More specifically, a CSP-based, syntax-oriented model construction, which requires the support of a theorem prover, is complemented by model extrapolation, via automata learning. This may support the systematic completion of the requirements, the nature of the requirement being partial, which provides focus on the most prominent scenarios. This may generalize requirement skeletons by extrapolation and may indicate by way of automatically generated traces where the requirement specification is too loose and additional information is required.

Systems, methods and apparatus are provided through which in some embodiments, automata learning algorithms and techniques are implemented to generate a more complete set of scenarios for requirements based programming. More specifically, a CSP-based, syntax-oriented model construction, which requires the support of a theorem prover, is complemented by model extrapolation, via automata learning. This may support the systematic completion of the requirements, the nature of the requirement being partial, which provides focus on the most prominent scenarios. This may generalize requirement skeletons by extrapolation and may indicate by way of automatically generated traces where the requirement specification is too loose and additional information is required.

Connectionist learning models have had considerable empirical success, but it is hard to characterize exactly what they learn. The learning of finite-state languages (FSL) from example strings is a domain which has been extensively studied and might provide an opportunity to help understand connectionist learning. A major problem is that traditional FSl learning assumes the storage of all examples and thus violates connectionist principles. This paper presents a provably correct algorithm for inferring any minimum-state deterministic finite-state automata (FSA) from a complete ordered sample using limited total storage and without storing example strings. The algorithm is an iterative strategy that uses at each stage a current encoding of the data considered so far, and one single sample string. One of the crucial advantages of our algorithm is that the total amount of space, used in the course of learning, for encoding any finite prefix of the sample is polynomial in the size of the inferred minimum state deterministic FSA. The algorithm is also relatively efficient in time and has been implemented. More importantly, there is connectionist version of the algorithm that preserves these properties. The connectionist version requires much more structure than the usual models and has not yet been implemented. But is does significantly extend the scope of connectionist learning systems and helps relate them to other paradigms. We also show that no machine with finite working storage can identify iteratively the FSL from arbitrary presentations.

We define a two-step learner for RFSAs based on an observation table by using an algorithm for minimal DFAs to build a table for the reversal of the language in question and showing that we can derive the minimal RFSA from it after some simple modifications. We compare the algorithm to two other table-based ones of which one (by Bollig et al. 2009) infers a RFSA directly, and the other is another two-step learner proposed by the author. We focus on the criterion of query complexity.

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We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the complexity of which is a longstanding open problem. Secondly, we derive lower bounds on the number of queries needed to learn multiplicity tree automata in Angluin's exact learning model, over both arbitrary and fixed fields. Habrard and Oncina (2006) give an exact learning algorithm for multiplicity tree automata, in which the number of queries is proportional to the size of the target automaton and the size of a largest counterexample, represented as a tree, that is returned by the Teacher. However, the smallest tree-counterexample may be exponential in the size of the target automaton. Thus the above algorithm does not run in time polynomial in the size of the target automaton, and has query complexity exponential in the lower bound. Assuming a Teacher that returns minimal DAG representations of counterexamples, we give a new exact learning algorithm whose query complexity is quadratic in the target automaton size, almost matching the lower bound, and improving the best previously-known algorithm by an exponential factor.

We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the complexity of which is a longstanding open problem. Secondly, we derive lower bounds on the number of queries needed to learn multiplicity tree automata in Angluin's exact learning model, over both arbitrary and fixed fields. Habrard and Oncina (2006) give an exact learning algorithm for multiplicity tree automata, in which the number of queries is proportional to the size of the target automaton and the size of a largest counterexample, represented as a tree, that is returned by the Teacher. However, the smallest tree-counterexample may be exponential in the size of the target automaton. Thus the above algorithm does not run in time polynomial in the size of the target automaton, and has query complexity exponential in the lower bound. Assuming a Teacher that returns minimal DAG representations of counterexamples, we give a new exact learning algorithm whose query complexity is quadratic in the target automaton size, almost matching the lower bound, and improving the best previously-known algorithm by an exponential factor.

We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the complexity of which is a longstanding open problem. Secondly, we derive lower bounds on the number of queries needed to learn multiplicity tree automata in Angluin's exact learning model, over both arbitrary and fixed fields. Habrard and Oncina (2006) give an exact learning algorithm for multiplicity tree automata, in which the number of queries is proportional to the size of the target automaton and the size of a largest counterexample, represented as a tree, that is returned by the Teacher. However, the smallest tree-counterexample may be exponential in the size of the target automaton. Thus the above algorithm does not run in time polynomial in the size of the target automaton, and has query complexity exponential in the lower bound. Assuming a Teacher that returns minimal DAG representations of counterexamples, we give a new exact learning algorithm whose query complexity is quadratic in the target automaton size, almost matching the lower bound, and improving the best previously-known algorithm by an exponential factor.

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability and hence optimizations that enable learning of compact representations are important. In this paper, we continue the development of a general framework for automata learning based on category theory and develop a class of optimizations and an accompanying correctness proof for learning algorithms. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. These side-effects are used to learn more compact automaton models and the abstract categorical approach enables us to capture several possible optimizations under the same (p)roof.

Consider a repeated two-person game. The question is how much smarter a player must be in order to effectively predict the moves of the other player. The answer depends on the formal definition of effective prediction, the number of actions each player has in the stage game, as well as on the measure of smartness. Effective prediction means that, no matter what the stage-game payoff function, the player can play (with high probability) a best reply in most stages. Neyman and Spencer [4] provide a complete asymptotic solution when smartness is measured by the size of the automata that implement the strategies: Let G = hI, J, gi be a two-person zero-sum game; I and J are the set of actions of player 1 and player 2 respectively, and g : I × J ! R is the payoff function to player 1. Consider the repeated two-person zero-sum game G(k,m) where player 1’s possible strategies are those implementable by an automaton with k states and player 2’s possible strategies are those implementable by an automaton with m states. We say that player 2 can effectively predict the moves of player 1 if for every reaction function r : I ! J player 2 has a strategy (in G(k,m)) such that for every strategy of player 1 the expected empirical distribution of the action pairs (i, j) is essentially supported on the set of action pairs of the form (i, r(i)). [4] characterizes. ©2007 Microsoft Corporation. All rights reserved.

As a general and thus popular model for autonomous systems, partially observable Markov decision process (POMDP) can capture uncertainties from different sources like sensing noises, actuation errors, and uncertain environments. However, its comprehensiveness makes the planning and control in POMDP difficult. Traditional POMDP planning problems target to find the optimal policy to maximize the expectation of accumulated rewards. But for safety critical applications, guarantees of system performance described by formal specifications are desired, which motivates us to consider formal methods to synthesize supervisor for POMDP. With system specifications given by Probabilistic Computation Tree Logic (PCTL), we propose a supervisory control framework with a type of deterministic finite automata (DFA), za-DFA, as the controller form. While the existing work mainly relies on optimization techniques to learn fixed-size finite state controllers (FSCs), we develop an $L^*$ learning based algorithm to determine both space and transitions of za-DFA. Membership queries and different oracles for conjectures are defined. The learning algorithm is sound and complete. An example is given in detailed steps to illustrate the supervisor synthesis algorithm.

Single channel based wireless networks have limited bandwidth and throughput and the bandwidth utilization decreases due to congestion and interference from other sources. In order to increase the throughput, transmission in multiple channels is considered as an option. In this paper, we propose a distributed dynamic channel allocation scheme using adaptive learning automata for wireless networks whose nodes are equipped with single radio interfaces. The proposed schemes, Adaptive Pursuit Reward-Inaction, Adaptive Pursuit Reward-Penalty, and Adaptive Pursuit Reward-Only, run periodically on the nodes, and adaptively find the suitable channel allocation in order to attain a desired performance. A novel performance index, which takes into account the throughput and the energy consumption, is considered. The proposed learning scheme is adaptive in the sense of updating rule. The update value of the probabilities in the each step is a function of the error in the performance index.

NOTE: Unfortunately the recording of this talk was cut short by 5 minutes because of over runs earlier in the conference program. Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics by Heitor Casagrande @QTMLConference

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This paper considers a class of reinforcement-learning that belongs to the family of Learning Automata and provides a stochastic-stability analysis in strategic-form games. For this class of dynamics, convergence to pure Nash equilibria has been demonstrated only for the fine class of potential games. Prior work primarily provides convergence properties of the dynamics through stochastic approximations, where the asymptotic behavior can be associated with the limit points of an ordinary-differential equation (ODE). However, analyzing global convergence through the ODE-approximation requires the existence of a Lyapunov or a potential function, which naturally restricts the applicabity of these algorithms to a fine class of games. To overcome these limitations, this paper introduces an alternative framework for analyzing stochastic-stability that is based upon an explicit characterization of the (unique) invariant probability measure of the induced Markov chain.

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