Showing papers on "Automata theory published in 2011"

Descriptional and computational complexity of finite automata---A survey

Abstract: Finite automata are probably best known for being equivalent to right-linear context-free grammars and, thus, for capturing the lowest level of the Chomsky-hierarchy, the family of regular languages. Over the last half century, a vast literature documenting the importance of deterministic, nondeterministic, and alternating finite automata as an enormously valuable concept has been developed. In the present paper, we tour a fragment of this literature. Mostly, we discuss developments relevant to finite automata related problems like, for example, (i) simulation of and by several types of finite automata, (ii) standard automata problems such as fixed and general membership, emptiness, universality, equivalence, and related problems, and (iii) minimization and approximation. We thus come across descriptional and computational complexity issues of finite automata. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved.

Enhancements of the bisimulation proof method

Abstract: Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

Advanced Topics in Bisimulation and Coinduction

Abstract: Coinduction is a method for specifying and reasoning about infinite data types and automata with infinite behaviour. In recent years, it has come to play an ever more important role in the theory of computing. It is studied in many disciplines, including process theory and concurrency, modal logic and automata theory. Typically, coinductive proofs demonstrate the equivalence of two objects by constructing a suitable bisimulation relation between them. This collection of surveys is aimed at both researchers and Master's students in computer science and mathematics and deals with various aspects of bisimulation and coinduction, with an emphasis on process theory. Seven chapters cover the following topics: history, algebra and coalgebra, algorithmics, logic, higher-order languages, enhancements of the bisimulation proof method, and probabilities. Exercises are also included to help the reader master new material.

Energy games in multiweighted automata

Abstract: Energy games have recently attracted a lot of attention. These are games played on finite weighted automata and concern the existence of infinite runs subject to boundary constraints on the accumulated weight, allowing e.g. only for behaviours where a resource is always available (nonnegative accumulated weight), yet does not exceed a given maximum capacity. We extend energy games to a multiweighted and parameterized setting, allowing us to model systems with multiple quantitative aspects. We present reductions between Petri nets and multiweighted automata and among different types of multiweighted automata and identify new complexity and (un)decidability results for both one- and two-player games. We also investigate the tractability of an extension of multiweighted energy games in the setting of timed automata.

Automata with Group Actions

Abstract: Our motivating question is a My hill-Nerode theorem for infinite alphabets. We consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order. We develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts, nominal sets are the special case of our framework where letters can be only compared for equality. We use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality, we obtain automata equivalent in expressive power to finite memory automata, as defined by Francez and Kaminski.

Fresh-register automata

Abstract: What is a basic automata-theoretic model of computation with names and fresh-name generation? We introduce Fresh-Register Automata (FRA), a new class of automata which operate on an infinite alphabet of names and use a finite number of registers to store fresh names, and to compare incoming names with previously stored ones. These finite machines extend Kaminski and Francez's Finite-Memory Automata by being able to recognise globally fresh inputs, that is, names fresh in the whole current run. We examine the expressivity of FRA's both from the aspect of accepted languages and of bisimulation equivalence. We establish primary properties and connections between automata of this kind, and answer key decidability questions. As a demonstrating example, we express the theory of the pi-calculus in FRA's and characterise bisimulation equivalence by an appropriate, and decidable in the finitary case, notion in these automata.

On Codiagnosability and Coobservability With Dynamic Observations

Abstract: Codiagnosability and coobservability in discrete event systems where observations are dynamic are considered. Instead of having a fixed set of observable events, the observation of an event is dynamic (trace-dependent) in this paper. A procedure is developed to transform the problem of coobservability to the problem of codiagnosability in the context of dynamic observations. This proves that problems of coobservability are transformable to problems of codiagnosability and enables us to leverage the large literature available for codiagnosability to solve problems of coobservability. Furthermore, in the case of dynamic observations, the known polynomial-complexity tests for the property of codiagnosability based on verifier automata with fixed observable event set(s) are no longer directly applicable. A new testing procedure is developed that can handle transition-based dynamic observations and remains of polynomial complexity in the state space of the system. This new testing procedure employs a covering of the state space of the system based on cluster automata, which enhances its computational efficiency. Based on cluster automata, a new type of verifier automaton is built, called the C-VERIFIER, for verification of codiagnosability. As an application of the above mentioned transformation, the C-VERIFIER becomes a unified method for verifying both codiagnosability and coobservability.

Symbolic Analysis of Sonar Data for Underwater Target Detection

Abstract: This paper presents a symbolic pattern analysis method for robust feature extraction from sidescan sonar images that are generated from autonomous underwater vehicles (AUVs). The proposed data-driven algorithm, built upon the concepts of symbolic dynamics and automata theory, is used for detection of mines and mine-like objects in the undersea environment. This real-time algorithm is based on symbolization of the data space via coarse graining, i.e., partitioning of the two-dimensional sonar images. The statistical information, in terms of stochastic matrices that serve as features, is extracted from the symbolized images by construction of probabilistic finite state automata. A binary classifier is designed for discrimination of detected objects into mine-like and nonmine-like categories. The pattern analysis algorithm has been validated on sonar images generated in the exploration phase of a mine hunting operation; these data have been provided by the Naval Surface Warfare Center. The algorithm is formulated for real-time execution on limited-memory commercial-of-the-shelf platforms and is capable of detecting objects on the seabed-bottom.

From computability to executability : a process-theoretic view on automata theory

Abstract: The theory of automata and formal language was devised in the 1930s to provide models for and to reason about computation. Here we mean by computation a procedure that transforms input into output, which was the sole mode of operation of computers at the time. Nowadays, computers are systems that interact with us and also each other; they are non-deterministic, reactive systems. Concurrency theory, split off from classical automata theory a few decades ago, provides a model of computation similar to the model given by the theory of automata and formal language, but focuses on concurrent, reactive and interactive systems. This thesis investigates the integration of the two theories, exposing the differences and similarities between them. Where automata and formal language theory focuses on computations and languages, concurrency theory focuses on behaviour. To achieve integration, we look for process-theoretic analogies of classic results from automata theory. The most prominent difference is that we use an interpretation of automata as labelled transition systems modulo (divergence-preserving) branching bisimilarity instead of treating automata as language acceptors. We also consider similarities such as grammars as recursive specifications and finite automata as labelled finite transition systems. We investigate whether the classical results still hold and, if not, what extra conditions are sufficient to make them hold. We especially look into three levels of Chomsky's hierarchy: we study the notions of finite-state systems, pushdown systems, and computable systems. Additionally we investigate the notion of parallel pushdown systems. For each class we define the central notion of automaton and its behaviour by associating a transition system with it. Then we introduce a suitable specification language and investigate the correspondence with the respective automaton (via its associated transition system). Because we not only want to study interaction with the environment, but also the interaction within the automaton, we make it explicit by means of communicating parallel components: one component representing the finite control of the automaton and one component representing the memory. First, we study finite-state systems by reinvestigating the relation between finite-state automata, left- and right-linear grammars, and regular expressions, but now up to (divergence-preserving) branching bisimilarity. For pushdown systems we augment the finite-state systems with stack memory to obtain the pushdown automata and consider different termination styles: termination on empty stack, on final state, and on final state and empty stack. Unlike for language equivalence, up to (divergence-preserving) branching bisimilarity the associated transition systems for the different termination styles fall into different classes. We obtain (under some restrictions) the correspondence between context-free grammars and pushdown automata for termination on final state and empty stack. We show how for contrasimulation, a weaker equivalence than branching bisimilarity, we can obtain the correspondence result without some of the restrictions. Finally, we make the interaction within a pushdown automaton explicit, but in a different way depending on the termination style. By analogy of pushdown systems we investigate the parallel pushdown systems, obtained by augmenting finite-state systems with bag memory, and consider analogous termination styles. We investigate the correspondence between context-free grammars that use parallel composition instead of sequential composition and parallel pushdown automata. While the correspondence itself is rather tight, it unfortunately only covers a small subset of the parallel pushdown automata, i.e. the single-state parallel pushdown automata. When making the interaction within parallel pushdown automata explicit, we obtain a rather uniform result for all termination styles. Finally, we study computable systems and the relation with exective and computable transition systems and Turing machines. For this we present the reactive Turing machine, a classical Turing machine augmented with capabilities for interaction. Again, we make the interaction in the reactive Turing machine between its finite control and the tape memory explicit.

On the Temporal Granularity in Fuzzy Cognitive Maps

Abstract: The theory of fuzzy cognitive maps (FCMs) is a powerful approach to modeling human knowledge that is based on causal reasoning. Taking advantage of fuzzy logic and cognitive map theories, FCMs enable system designers to model complex frameworks by defining degrees of causality between causal objects. They can be used to model and represent the behavior of simple and complex systems by capturing and emulating the human being to describe and present systems in terms of tolerance, imprecision, and granulation of information. However, FCMs lack the temporal concept that is crucial in many real-world applications, and they do not offer formal mechanisms to verify the behavior of systems being represented, which limit conventional FCMs in knowledge representation. In this paper, we present an extension to FCMs by exploiting a theory from formal languages, namely, the timed automata, which bridges the aforementioned inadequacies. Indeed, the theory of timed automata enables FCMs to effectively deal with a double-layered temporal granularity, extending the standard idea of B-time that characterizes the iterative nature of a cognitive inference engine and offering model checking techniques to test the cognitive and dynamic comportment of the framework being designed.

Cybernetics, Automata Studies, and the Dartmouth Conference on Artificial Intelligence

Abstract: The Dartmouth Summer Research Project on Artificial Intelligence, held at Datrmouth College in 1956, is regarded as the official "birthplace" of Al. This article draws on unpublished archives to shed new light on the origins of the conference and the complex relationships between cybernetics, automata studies, and Al in the 1950s.

Identifying behavior models for process plants

Abstract: The increasing complexity of today's production systems and the variety of model-based approaches to their monitoring, diagnosis and testing emphasize the importance of the modeling step. Modeling is mostly done manually, in a costly and time-consuming way. In this paper, an alternative that comes from the learning theory is given: an automated procedure for identifying behavior models from recorded observations. Assuming the system's structure is known, the algorithm presented here is capable of learning behavior models for its components. The algorithm accounts for probabilistic, timing, discrete and continuous aspects of the given system, using the modeling formalism of hybrid automata. The practical usability of identified models is demonstrated using an anomaly detection application for a real production system.

Forest automata for verification of heap manipulation

Abstract: We consider verification of programs manipulating dynamic linked data structures such as various forms of singly and doubly-linked lists or trees. We consider important properties for this kind of systems like no null-pointer dereferences, absence of garbage, shape properties, etc. We develop a verification method based on a novel use of tree automata to represent heap configurations. A heap is split into several "separated" parts such that each of them can be represented by a tree automaton. The automata can refer to each other allowing the different parts of the heaps to mutually refer to their boundaries. Moreover, we allow for a hierarchical representation of heaps by allowing alphabets of the tree automata to contain other, nested tree automata. Program instructions can be easily encoded as operations on our representation structure. This allows verification of programs based on a symbolic state-space exploration together with refinable abstraction within the so-called abstract regular tree model checking. A motivation for the approach is to combine advantages of automata-based approaches (higher generality and flexibility of the abstraction) with some advantages of separation-logic-based approaches (efficiency). We have implemented our approach and tested it successfully on multiple non-trivial case studies.

A multi-encoding approach for LTL symbolic satisfiability checking

Abstract: Formal behavioral specifications written early in the system-design process and communicated across all design phases have been shown to increase the efficiency, consistency, and quality of the system under development. To prevent introducing design or verification errors, it is crucial to test specifications for satisfiability. Our focus here is on specifications expressed in linear temporal logic (LTL). We introduce a novel encoding of symbolic transition-based Buchi automata and a novel, "sloppy," transition encoding, both of which result in improved scalability. We also define novel BDD variable orders based on tree decomposition of formula parse trees. We describe and extensively test a new multi-encoding approach utilizing these novel encoding techniques to create 30 encoding variations. We show that our novel encodings translate to significant, sometimes exponential, improvement over the current standard encoding for symbolic LTL satisfiability checking.

Expressiveness of propositional projection temporal logic with star

Abstract: This paper investigates the expressiveness of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Buchi automata and @w-regular expressions are first extended as Stutter Buchi Automata (SBA) and Extended Regular Expressions (ERE) to include both finite and infinite strings. Further, by equivalent transformations among PPTL* formulas, SBAs and EREs, PPTL* is proved to represent exactly the full regular language. Moreover, some fragments of PPTL* are characterized, and finally, PPTL* and its fragments are classified into five different language classes.

Fifty years of automata simulation: a review

Abstract: Automata theory is an important subject in computer science and quite consequently, simulation of automata for pedagogical purposes is an important topic in computer science education research. This article reviews the major initiatives in the field of simulation of automata in the last five decades with emphasis on those automata simulators actually used at universities for teaching. A classification of the automata simulators on the basis of their design paradigms has been developed where they have been classified broadly into language based automata simulators and visualization centric automata simulators. Some salient trends in the research on simulation of automata are also identified. The article concludes with an advocacy for continuing research on simulation of automata and integration of automata simulators in teaching.

Green's relations and their use in automata theory

Abstract: The objective of this survey is to present the ideal theory of monoids, the so-called Green's relations, and to illustrate the usefulness of this tool for solving automata related questions. We use Green's relations for proving four classical results related to automata theory: The result of Schutzenberger characterizing star-free languages, the theorem of factorization forests of Simon, the characterization of infinite words of decidable monadic theory due to Semenov, and the result of determinization of automata over infinite words of McNaughton.

Automata-based presentations of infinite structures

Abstract: Finite presentations of infinite structures The model theory of finite structures is intimately connected to various fields in computer science, including complexity theory, databases, and verification. In particular, there is a close relationship between complexity classes and the expressive power of logical languages, as witnessed by the fundamental theorems of descriptive complexity theory, such as Fagin's Theorem and the Immerman-Vardi Theorem (see [78, Chapter 3] for a survey). However, for many applications, the strict limitation to finite structures has turned out to be too restrictive, and there have been considerable efforts to extend the relevant logical and algorithmic methodologies from finite structures to suitable classes of infinite ones. In particular this is the case for databases and verification where infinite structures are of crucial importance [130]. Algorithmic model theory aims to extend in a systematic fashion the approach and methods of finite model theory, and its interactions with computer science, from finite structures to finitely-presentable infinite ones. There are many possibilities to present infinite structures in a finite manner. A classical approach in model theory concerns the class of computable structures ; these are countable structures, on the domain of natural numbers, say, with a finite collection of computable functions and relations. Such structures can be finitely presented by a collection of algorithms, and they have been intensively studied in model theory since the 1960s. However, from the point of view of algorithmic model theory the class of computable structures is problematic.

Robustness in real-time systems

Abstract: We review several aspects of robustness of real-time systems, and present recent results on the robust verification of timed automata.

Quantitative Languages Defined by Functional Automata

Abstract: A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio. We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. The results on functionality and determinizability are expressed for the more general class of functional group automata. This allows one to formulate within the same framework new results related to discounted sum automata and known results on sum and mean automata. Ratio automata do not fit within this general scheme and different techniques are required to decide functionality.

A path algebra for multi-relational graphs

Abstract: A multi-relational graph maintains two or more relations over a vertex set. This article defines an algebra for traversing such graphs that is based on an n-ary relational algebra, a concatenative single-relational path algebra, and a tensor-based multi-relational algebra. The presented algebra provides a monoid, automata, and formal language theoretic foundation for the construction of a multi-relational graph traversal engine.

Weighted tree automata over valuation monoids and their characterization by weighted logics

Abstract: Quantitative aspects of systems can be modeled by weighted automata. Here, we deal with such automata running on finite trees. Usually, transitions are weighted with elements of a semiring and the behavior of the automaton is obtained by multiplying the weights along a run. We turn to a more general cost model: the weight of a run is now determined by a global valuation function. An example of such a valuation function is the average of the weights. We establish a characterization of the behaviors of these weighted finite tree automata by fragments of weighted monadic second-order logic. For bi-locally finite bimonoids, we show that weighted tree automata capture the expressive power of several semantics of full weighted MSO logic. Decision procedures follow as consequences.

Optimizing Voting Rule for Cooperative Spectrum Sensing Through Learning Automata

Abstract: In cooperative spectrum sensing (CSS), an optimal decision fusion rule can effectively improve the performance of the secondary system. Considering that a priori knowledge about the characteristics of primary users and secondary users (SUs) is usually unknown in practice, we propose a learning automata-based algorithm to derive the optimal voting rule for decision fusion in CSS. The proposed algorithm can work with any detection method used at SUs. Its convergence and robustness are shown here. Its stability is also analyzed by using noncooperative game theory. The condition that the obtained optimal voting rule remains unchanged is derived based on the concept of subgame perfect Nash equilibrium. It is shown that the proposed algorithm generally does not need to run many times and can work at a low cost in practice. Computer simulations validate the effectiveness of the proposed scheme.

Learning of Automata Models Extended with Data

Abstract: One of the challenges in the Connect project is to develop techniques for learning models of networked components from exploratory interaction with the component, based on analyzing messages exchanged between the component and its environment. Many approaches to this problem employ regular inference (aka. automata learning) techniques which generate modest-size finite-state models. Most communication with real-life systems involves data values being relevant to the communication context and thus influencing the observable behavior of the communication endpoints. When applying methods from the realm of automata learning, it is desirable to handle such data-occurrences. It is therefore important to extend inference techniques to handle message alphabets and state-spaces with structures containing data parameters, often with large domains. After very briefly mentioning several approaches to the problem, we give a longer account of an approach proposed by Aarts et al, which adapts ideas from of predicate abstraction, successfully used in formal verification. We illustrate the techniques by application to a simple running example, which models a simple booking service.