Showing papers on "Automata theory published in 2016"

Multiparty Session Types Within a Canonical Binary Theory, and Beyond

Abstract: A widespread approach to software service analysis uses session types. Very different type theories for binary and multiparty protocols have been developed; establishing precise connections between them remains an open problem. We present the first formal relation between two existing theories of binary and multiparty session types: a binary system rooted in linear logic, and a multiparty system based on automata theory. Our results enable the analysis of multiparty protocols using a much simpler type theory for binary protocols, ensuring protocol fidelity and deadlock-freedom. As an application, we offer the first theory of multiparty session types with behavioral genericity. This theory is natural and powerful; its analysis techniques reuse results for binary session types.

Automata Theory Meets Barrier Certificates: Temporal Logic Verification of Nonlinear Systems

Abstract: We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based verification allows the decomposition the verification task into a finite collection of simpler constraints over the continuous state space. The satisfaction of these constraints in turn can be (potentially conservatively) proved by appropriately constructed barrier certificates. As a result, our approach, together with optimization-based search for barrier certificates, allows computational verification of dynamical systems against temporal logic properties while avoiding explicit abstractions of the dynamics as commonly done in literature.

Computer Science Education for Primary and Lower Secondary School Students: Teaching the Concept of Automata

Abstract: We explore the feasibility of early introduction to automata theory through gamification. We designed a puzzle game that players can answer correctly if they understand the fundamental concepts of automata theory. In our investigation, 90 children played the game, and their actions were recorded in play logs. An analysis of the play logs shows that approximately 60p of the children achieved correct-answer rates of at least 70p, which suggests that primary and lower secondary school students can understand the fundamental concepts of automata theory. Meanwhile, our analysis shows that most of them do not fully understand automata theory, but some of them have a good understanding of the concept.

Solving Parity Games via Priority Promotion

Abstract: We consider parity games, a special form of two-player infinite-duration games on numerically labelled graphs, whose winning condition requires that the maximal value of a label occurring infinitely often during a play be of some specific parity. The problem has a rather intriguing status from a complexity theoretic viewpoint, since it belongs to the class Open image in new window , and still open is the question whether it can be solved in polynomial time. Parity games also have great practical interest, as they arise in many fields of theoretical computer science, most notably logic, automata theory, and formal verification. In this paper, we propose a new algorithm for the solution of the problem, based on the idea of promoting vertices to higher priorities during the search for winning regions. The proposed approach has nice computational properties, exhibiting the best space complexity among the currently known solutions. Experimental results on both random games and benchmark families show that the technique is also very effective in practice.

Markov Chains and Unambiguous Büchi Automata

Abstract: Unambiguous automata, i.e., nondeterministic automata with the restriction of having at most one accepting run over a word, have the potential to be used instead of deterministic automata in settings where nondeterministic automata can not be applied in general. In this paper, we provide a polynomially time-bounded algorithm for probabilistic model checking of discrete-time Markov chains against unambiguous Buchi automata specifications and report on our implementation and experiments.

Automata theory meets approximate dynamic programming: Optimal control with temporal logic constraints

Abstract: We investigate the synthesis of optimal controllers for continuous-time and continuous-state systems under temporal logic specifications. The specification is expressed as a deterministic, finite automaton (the specification automaton) with transition costs, and the optimal system behavior is captured by a cost function that is integrated over time. We construct a dynamic programming problem over the product of the underlying continuous-time, continuous-state system and the discrete specification automaton. To solve this dynamic program, we propose controller synthesis algorithms based on approximate dynamic programming (ADP) for both linear and nonlinear systems under temporal logic constraints. We argue that ADP allows treating the synthesis problem directly, without forming expensive discrete abstractions. We show that, for linear systems under co-safe temporal logic constraints, the ADP solution reduces to a single semidefinite program.

Complementing Semi-deterministic Büchi Automata

Abstract: We introduce an efficient complementation technique for semi-deterministic Buchi automata, which are Buchi automata that are deterministic in the limit: from every accepting state onward, their behaviour is deterministic. It is interesting to study semi-deterministic automata, because they play a role in practical applications of automata theory, such as the analysis of Markov decision processes. Our motivation to study their complementation comes from the termination analysis implemented in Ultimate Buchi Automizer, where these automata represent checked runs and have to be complemented to identify runs to be checked. We show that semi-determinism leads to a simpler complementation procedure: an extended breakpoint construction that allows for symbolic implementation. It also leads to significantly improved bounds as the complement of a semi-deterministic automaton with n states has less than $$4^n$$ states. Moreover, the resulting automaton is unambiguous, which again offers new applications, like the analysis of Markov chains. We have evaluated our construction against the semi-deterministic automata produced by the Ultimate Buchi Automizer. The evaluation confirms that our algorithm outperforms the known complementation techniques for general nondeterministic Buchi automata.

From LTL to deterministic automata

Abstract: We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula $$\varphi $$ź. The automaton is the product of a co-Buchi automaton for $$\varphi $$ź and an array of Rabin automata, one for each $${\mathbf {G}}$$G-subformula of $$\varphi $$ź. The Rabin automaton for $${\mathbf {G}}\psi $$Gź is in charge of recognizing whether $${\mathbf {F}}{\mathbf {G}}\psi $$FGź holds. This information is passed to the co-Buchi automaton that decides on acceptance. As opposed to standard procedures based on Safra's determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.

Decision Problems for Parametric Timed Automata

Abstract: Parametric timed automata (PTAs) allow to reason on systems featuring concurrency and timing constraints making use of parameters. Most problems are undecidable for PTAs, including the parametric reachability emptiness problem, i.e., whether at least one parameter valuation allows to reach some discrete state. In this paper, we first exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Second, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses.

Symbolic Optimal Reachability in Weighted Timed Automata

Abstract: Weighted timed automata have been defined in the early 2000 s for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm has been developed to solve that problem. This algorithm uses so-called priced zones, an extension of standard zones with cost functions. In order to ensure termination, the algorithm requires clocks to be bounded. For unpriced timed automata, much work has been done to develop sound abstractions adapted to the forward exploration of timed automata, ensuring termination of the model-checking algorithm without bounding the clocks. In this paper, we take advantage of recent developments on abstractions for timed automata, and propose an algorithm allowing for symbolic analysis of all weighted timed automata, without requiring bounded clocks.

Topics in Grammatical Inference

Abstract: This book explains advanced theoretical and application-related issues in grammatical inference, a research area inside the inductive inference paradigm for machine learning. The first three chapters of the book deal with issues regarding theoretical learning frameworks; the next four chapters focus on the main classes of formal languages according to Chomsky's hierarchy, in particular regular and context-free languages; and the final chapter addresses the processing of biosequences. The topics chosen are of foundational interest with relatively mature and established results, algorithms and conclusions. The book will be of value to researchers and graduate students in areas such as theoretical computer science, machine learning, computational linguistics, bioinformatics, and cognitive psychology who are engaged with the study of learning, especially of the structure underlying the concept to be learned. Some knowledge of mathematics and theoretical computer science, including formal language theory, automata theory, formal grammars, and algorithmics, is a prerequisite for reading this book.

Minimal Separating Sequences for All Pairs of States

Abstract: Finding minimal separating sequences for all pairs of inequivalent states in a finite state machine is a classic problem in automata theory. Sets of minimal separating sequences, for instance, play a central role in many conformance testing methods. Moore has already outlined a partition refinement algorithm that constructs such a set of sequences in \(\mathcal {O}(mn)\) time, where m is the number of transitions and n is the number of states. In this paper, we present an improved algorithm based on the minimization algorithm of Hopcroft that runs in \(\mathcal {O}(m \log n)\) time. The efficiency of our algorithm is empirically verified and compared to the traditional algorithm.

Automata-theoretic protocol programming

Abstract: Parallel programming has become essential for writing scalable programs on general hardware. Conceptually, every parallel program consists of workers, which implement primary units of sequential computation, and protocols, which implement the rules of interaction that workers must abide by. As programmers have been writing sequential code for decades, programming workers poses no new fundamental challenges. What is new---and notoriously difficult---is programming of protocols. In this thesis, I study an approach to protocol programming where programmers implement their workers in an existing general-purpose language (GPL), while they implement their protocols in a complementary domain-specific language (DSL). DSLs for protocols enable programmers to express interaction among workers at a higher level of abstraction than the level of abstraction supported by today's GPLs, thereby addressing a number of protocol programming issues with today's GPLs. In particular, in this thesis, I develop a DSL for protocols based on a theory of formal automata and their languages. The specific automata that I consider, called constraint automata, have transition labels with a richer structure than alphabet symbols in classical automata theory. Exactly these richer transition labels make constraint automata suitable for modeling protocols.

Completely Reachable Automata

Abstract: We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.

On the Synchronizing Probability Function and the Triple Rendezvous Time for Synchronizing Automata

Abstract: The Cerný conjecture is a longstanding open problem in automata theory. We study two different concepts, which allow us to approach it from a new angle. The first one is the triple rendezvous time, i.e., the length of the shortest word mapping three states onto a single one. The second one is the synchronizing probability function of an automaton, a recently introduced tool which reinterprets the synchronizing phenomenon as a two-player game and allows us to obtain optimal strategies through a linear program. Our contribution is twofold. First, by coupling two different novel approaches based on the synchronizing probability function and properties of linear programming, we obtain a new upper bound on the triple rendezvous time. Second, by exhibiting a family of counterexamples, we disprove a conjecture on the growth of the synchronizing probability function. We then suggest natural follow-ups toward the Cerný conjecture.

Towards a voxel-based geographic automata for the simulation of geospatial processes

Abstract: Many geographic processes evolve in a three dimensional space and time continuum. However, when they are represented with the aid of geographic information systems (GIS) or geosimulation models they are modelled in a framework of two-dimensional space with an added temporal component. The objective of this study is to propose the design and implementation of voxel-based automata as a methodological approach for representing spatial processes evolving in the four-dimensional (4D) space–time domain. Similar to geographic automata models which are developed to capture and forecast geospatial processes that change in a two-dimensional spatial framework using cells (raster geospatial data), voxel automata rely on the automata theory and use three-dimensional volumetric units (voxels). Transition rules have been developed to represent various spatial processes which range from the movement of an object in 3D to the diffusion of airborne particles and landslide simulation. In addition, the proposed 4D models demonstrate that complex processes can be readily reproduced from simple transition functions without complex methodological approaches. The voxel-based automata approach provides a unique basis to model geospatial processes in 4D for the purpose of improving representation, analysis and understanding their spatiotemporal dynamics. This study contributes to the advancement of the concepts and framework of 4D GIS.

Quantum Actin Automata and Three-Valued Logics

Abstract: Actin is a filament-forming protein responsible for communication, information processing and decision making in eukariotic cells. To show how computation can be implemented on actin filaments we model actin as a helix of two 1-D quantum automata arrays. The model advances our previous work by exploiting the quantum aspects of the automaton (superposition). We use selected functions of automaton state transitions to compute examples of actin automata evolution and to realize three-valued logical gates in the actin automata. Implementation of operators of several three-valued logical systems is demonstrated on examples. Our results lay a ground for theoretical studies, and possible future experimental laboratory implementations of multiple-valued logical circuits.

Bisimulation for BL-general fuzzy automata

Abstract: In this note, we define bisimulation for BL-general fuzzy automata and show that if there is a bisimulation between two BL-general fuzzy automata, then they have the same behavior.For a given BL-general fuzzy automata, we obtain the greatest bisimulation for the BL-general fuzzy automata. Thereafter, if we use the greatest bisimulation, then we obtain a quotient BL-general fuzzy automata and this quotient is minimal, furthermore there is a morphism from the first one to its quotient.Also, for two given BL-general fuzzy automata we present an algorithm, which determines bisimulation between them.Finally, we present some examples to clarify these new notions.

Algorithmic Techniques for Solving Graph Problems on the Automata Processor

Abstract: The Automata Processor is a new accelerator technology that supports direct hardware implementation of a set of non-deterministic finite automata over a streaming input, and is designed for complex string pattern matching applications. In this paper, we broaden the scope of this architecture beyond its primary design goal, by developing algorithmic techniques to solve problems on unweighted graphs. We present a strategy to represent nodes and edges in a graph using strings, and use this transformation to develop algorithms for several classic graph problems including finding Hamiltonian paths and cycles, connected components, and breadth-first search. Our algorithms rely on a core set of automata building blocks which we designed for this purpose, and illustrate various design considerations that developers must bear in mind when harnessing this new technology. We expect that this work provides the foundations for solving graph problems using the Automata Processor.

Similarity-based minimization of fuzzy tree automata

Abstract: This paper presents a contribution to the problem of similarity-based minimization of deterministic fuzzy finite tree automata (DFFTA). The main question is: how to minimize the number of states of a complete and reduced DFFTA such that the languages of the original automaton and the minimized one be similar but not necessarily equal? Based on extended concepts of fuzzy distance and similarity measures on L-fuzzy sets, we introduce the notion of similarity-based minimal (s-minimal) DFFTA which approximately accepts a fuzzy tree language. Then, a solution for handeling the trade-off between the amount of reduction and the quality of preserving the behavior of system is presented. The paper deals with fuzzy tree automata over complete lattices, but identical results can also be obtained in a more general context for fuzzy tree automata over complete residuated lattices, lattice-ordered monoids, and even for weighted automata over commutative semirings.

Comparison of max-plus automata and joint spectral radius of tropical matrices

Abstract: Weighted automata over the max-plus semiring S are closely related to finitely generated semigroups of matrices over S. In this paper, we use results in automata theory to study two quantities associated with sets of matrices: the joint spectral radius and the ultimate rank. We prove that these two quantities are not computable over the tropical semiring, i.e. there is no algorithm that takes as input a finite set of matrices M and provides as output the joint spectral radius (resp. the ultimate rank) of M. On the other hand, we prove that the joint spectral radius is nevertheless approximable and we exhibit restricted cases in which the joint spectral radius and the ultimate rank are computable. To reach this aim, we study the problem of comparing functions computed by weighted automata over the tropical semiring. This problem is known to be undecidable and we prove that it remains undecidable in some specific subclasses of automata.

Language Recognition Power and Succinctness of Affine Automata

Abstract: In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz [6] referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the characterization of all regular unary languages recognized by two-state affine automata.

Monoids as Storage Mechanisms

Abstract: Automata theory has given rise to a variety of automata models that consist of a finite-state control and an infinite-state storage mechanism The aim of this work is to provide insights into how the structure of the storage mechanism influences the expressiveness and the analyzability of the resulting model To this end, it presents generalizations of results about individual storage mechanisms to larger classes These generalizations characterize those storage mechanisms for which the given result remains true and for which it fails In order to speak of classes of storage mechanisms, we need an overarching framework that accommodates each of the concrete storage mechanisms we wish to address Such a framework is provided by the model of valence automata, in which the storage mechanism is represented by a monoid Since the monoid serves as a parameter to specifying the storage mechanism, our aim translates into the question: For which monoids does the given (automata-theoretic) result hold? As a first result, we present an algebraic characterization of those monoids over which valence automata accept only regular languages In addition, it turns out that for each monoid, this is the case if and only if valence grammars, an analogous grammar model, can generate only context-free languages Furthermore, we are concerned with closure properties: We study which monoids result in a Boolean closed language class For every language class that is closed under rational transductions (in particular, those induced by valence automata), we show: If the class is Boolean closed and contains any non-regular language, then it already includes the whole arithmetical hierarchy This work also introduces the class of graph monoids, which are defined by finite graphs By choosing appropriate graphs, one can realize a number of prominent storage mechanisms, but also combinations and variants thereof Examples are pushdowns, counters, and Turing tapes We can therefore relate the structure of the graphs to computational properties of the resulting storage mechanisms In the case of graph monoids, we study (i) the decidability of the emptiness problem, (ii) which storage mechanisms guarantee semilinear Parikh images, (iii) when silent transitions (ie those that read no input) can be avoided, and (iv) which storage mechanisms permit the computation of downward closures

Walking on Data Words

Abstract: Data words are words with additional edges that connect pairs of positions carrying the same data value. We consider a natural model of automaton walking on data words, called Data Walking Automaton, and study its closure properties, expressiveness, and the complexity of some basic decision problems. Specifically, we show that the class of deterministic Data Walking Automata is closed under all Boolean operations, and that the class of non-deterministic Data Walking Automata has decidable emptiness, universality, and containment problems. We also prove that deterministic Data Walking Automata are strictly less expressive than non-deterministic Data Walking Automata, which in turn are captured by Class Memory Automata.

On Finite and Polynomial Ambiguity of Weighted Tree Automata

Abstract: We consider finite and polynomial ambiguity of weighted tree automata. Concerning finite ambiguity, we show that a finitely ambiguous weighted tree automaton can be decomposed into a sum of unambiguous automata. For polynomial ambiguity, we show how to decompose a polynomially ambiguous weighted tree automaton into simpler polynomially ambiguous automata and then analyze the structure of these simpler automata. We also outline how these results can be used to capture the ambiguity of weighted tree automata with weighted logics.

A new distributed learning automata based algorithm for maximum independent set problem

Abstract: Maximum independent set problem is an NP-Hard one with the aim of finding the set of independent vertices with maximum possible cardinality in a graph. In this paper, we investigate a learning automaton based algorithm that finds a maximum independent set in the graph. Initially, a learning automaton is assigned to each vertex of graph. In order to find candidate independent set, a set of distributed learning automata collaborate with each other. The proposed algorithm based on learning automata is guided iteratively to the maximum independent set by updating the action probability vector. In order to study the performance of the proposed algorithm, we conducted some experiments. The reported numerical results confirm the superiority of our proposed algorithm in terms of cardinality of the obtained solution.