Showing papers on "Automata theory published in 2010"

Noncommutative Rational Series with Applications

Abstract: The algebraic theory of automata was created by Schutzenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory to noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability. For example, number-theoretic results can now be more fully explored, in addition to applications in automata theory, codes and non-commutative algebra. Much material, for example, Schutzenberger's theorem on polynomially bounded rational series, appears here for the first time in book form. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap.

Strategy logic

Abstract: We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to specify properties of nonzero-sum games in a simple and natural way. We show that the one-alternation fragment of strategy logic is strong enough to express the existence of Nash equilibria and secure equilibria, and subsumes other logics that were introduced to reason about games, such as ATL, ATL^*, and game logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is nonelementary, for the simple fragment that is used above we show that the complexity is polynomial in the size of the game graph and optimal in the size of the formula (ranging from polynomial to 2EXPTIME depending on the form of the formula).

Quantitative languages

Abstract: Quantitative generalizations of classical languages, which assign to each word a real number instead of a Boolean value, have applications in modeling resource-constrained computation. We use weighted automata (finite automata with transition weights) to define several natural classes of quantitative languages over finite and infinite words; in particular, the real value of an infinite run is computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We define the classical decision problems of automata theory (emptiness, universality, language inclusion, and language equivalence) in the quantitative setting and study their computational complexity. As the decidability of the language-inclusion problem remains open for some classes of weighted automata, we introduce a notion of quantitative simulation that is decidable and implies language inclusion. We also give a complete characterization of the expressive power of the various classes of weighted automata. In particular, we show that most classes of weighted automata cannot be determinized.

Symbolic dynamics

Abstract: This chapter presents some of the links between automata theory and symbolic dynamics The emphasis is on two particular points The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type The second one is the connection between syntactic semigroups and the classification of sofic shifts up to conjugacy

Driver Steering Assistance for Lane-Departure Avoidance Based on Hybrid Automata and Composite Lyapunov Function

Abstract: This paper presents the design and the practical implementation of vehicle steering assistance that helps the driver avoid unintended lane departure. A switching strategy is built to govern the driver-assistance interaction, and the resulting hybrid system is formalized as an input/output (I/O) hybrid automaton. Composite Lyapunov functions, polyhedral-like invariant sets, and linear matrix inequality (LMI) methods constitute the heart of the approach used to design the lane-departure avoidance (LDA) system. The practical implementation of this steering assistance in a prototype vehicle confirms the effectiveness of this approach.

Learning I/O automata

Abstract: Links are established between three widely used modeling frameworks for reactive systems: the ioco theory of Tretmans, the interface automata of De Alfaro and Henzinger, and Mealy machines. It is shown that, by exploiting these links, any tool for active learning of Mealy machines can be used for learning I/O automata that are deterministic and output determined. The main idea is to place a transducer in between the I/O automata teacher and the Mealy machine learner, which translates concepts from the world of I/O automata to the world of Mealy machines, and vice versa. The transducer comes equipped with an interface automaton that allows us to focus the learning process on those parts of the behavior that can effectively be tested and/or are of particular interest. The approach has been implemented on top of the LearnLib tool and has been applied successfully to three case studies.

libalf: the automata learning framework

Abstract: This paper presents libalf, a comprehensive, open-source library for learning formal languages libalf covers various well-known learning techniques for finite automata (eg Angluin's L*, Biermann, RPNI etc) as well as novel learning algorithms (such as for NFA and visibly one-counter automata) libalf is flexible and allows facilely interchanging learning algorithms and combining domain-specific features in a plug-and-play fashion Its modular design and C++ implementation make it a suitable platform for adding and engineering further learning algorithms for new target models (eg, Buchi automata)

Quantum Automata with Open Time Evolution

Abstract: In this paper, a model for finite automaton with an open quantum evolution is introduced, and its basic properties are studied. It is shown that the (fuzzy) languages accepted by open evolution quantum automata obey various closure properties. More importantly, it is shown that major other models of finite automata, including probabilistic, measure once quantum, measure many quantum, and Latvian quantum automata can be simulated by the open quantum evolution automata without increasing the number of the states.

Variable automata over infinite alphabets

Abstract: Automated reasoning about systems with infinite domains requires an extension of regular automata to infinite alphabets. Existing formalisms of such automata cope with the infiniteness of the alphabet by adding to the automaton a set of registers or pebbles, or by attributing the alphabet by labels from an auxiliary finite alphabet that is read by an intermediate transducer. These formalisms involve a complicated mechanism on top of the transition function of automata over finite alphabets and are therefore difficult to understand and to work with. We introduce and study variable finite automata over infinite alphabets (VFA). VFA form a natural and simple extension of regular (and ω-regular) automata, in which the alphabet consists of letters as well as variables that range over the infinite alphabet domain. Thus, VFAs have the same structure as regular automata, only that some of the transitions are labeled by variables. We compare VFA with existing formalisms, and study their closure properties and classical decision problems. We consider the settings of both finite and infinite words. In addition, we identify and study the deterministic fragment of VFA. We show that while this fragment is sufficiently strong to express many interesting properties, it is closed under union, intersection, and complementation, and its nonemptiness and containment problems are decidable. Finally, we describe a determinization process for a determinizable subset of VFA.

Succinctness of two-way probabilistic and quantum finite automata

Abstract: We introduce a new model of two-way finite automaton, which is endowed with the capability of resetting the position of the tape head to the left end of the tape in a single move during the computation. Several variants of this model are examined, with the following results: The weakest known model of computation where quantum computers recognize more languages with bounded error than their classical counterparts is identified. We prove that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions (1PFAs and 1QFAs), and two-way nondeterministic finite automata (2NFAs). For this purpose, we demonstrate several infinite families of regular languages which can be recognized with some fixed probability greater than 1 2 by just tuning the transition amplitudes of a 2QFA (and, in one case, a 2PFA) with a constant number of states, whereas the sizes of the corresponding 1PFAs, 1QFAs and 2NFAs grow without bound. We also show that 2QFAs with mixed states can support highly efficient probability amplification.

Efficient Identification of Timed Automata: Theory and practice

Abstract: This thesis contains a study in a subfield of artificial intelligence, learning theory, machine learning, and statistics, known as system (or language) identification. System identification is concerned with constructing (mathematical) models from observations. Such a model is an intuitive description of a complex system. One of the main nice properties of models is that they can be visualized and inspected in order to provide insight into the different behaviors of a system. In addition, they can be used to perform different calculations, such as making predictions, analyzing properties, diagnosing errors, performing simulations, and many more. Models are therefore extremely useful tools for understanding, interpreting, and modifying different kinds of systems. Unfortunately, it can be very difficult to construct a model by hand. This thesis investigates the difficulty of automatically identifying models from observations. Observations of some process and its environment are given. These observations form sequences of events. Using system identification, we try to discover the logical structure underlying these event sequences. A well-known model of such a logical structure is the deterministic finite state automaton (DFA). A DFA is a language model. Hence, its identification (or inference) problem has been well studied in the grammatical inference field. Knowing this, we want to take an established method to learn a DFA and apply it to our event sequences. However, when observing a system there often is more information than just the sequence of symbols (events): the time at which these symbols occur is also available. A DFA can be used to model this time information implicitly. A disadvantage of such an approach is that it can result in an exponential blowup of both the input data and the resulting size of the model. In this thesis, we propose a different method that uses the time information directly in order to produce a timed model. We use a well-known DFA variant that includes the notion of time, called the timed automaton (TA). TAs are commonly used to model and reason about real-time systems. A TA models the timed information explicitly, i.e., using numbers. Because numbers use a binary representation of time, such an explicit representation can result in exponentially more compact models than an implicit representation. Therefore, also the time, space, and data required to identify TAs can be exponentially smaller than the time, space, and data required to identify DFAs. This efficiency argument is our main reason we are interested in identifying TAs. The work in this thesis makes four major contributions to the state-of-the-art on this topic: 1. It contains a thorough theoretical study of the complexity of identifying TAs from data. 2. It provides an algorithm for identifying a simple TA from labeled data, i.e., from event sequences for which it is known to which type of system behavior they belong. 3. It extends this algorithm to the setting of unlabeled data, i.e., from event sequences with unknown behaviors. 4. It shows how to apply this algorithm to the problem of identifying a real-time monitoring system. These contributions are of importance for anyone who is interested in identifying timed systems. Most importantly, both in our theoretical work and in our experiments we show that identifying a TA by using the time information directly is more efficient than identifying an equivalent DFA. In addition, our techniques can be applied to many interesting problems due to their generality. Examples are gaining insight into a real-time process, recognizing different process behaviors, identifying process models, and analyzing black-box systems.

Generalizing the powerset construction, coalgebraically

Abstract: Coalgebra is an abstract framework for the uniform study of different kinds of dynamical systems. An endofunctor $F$ determines both the type of systems ($F$-coalgebras) and a notion of behavioral equivalence ($\sim_F$) amongst them. Many types of transition systems and their equivalences can be captured by a functor $F$. For example, for deterministic automata the derived equivalence is language equivalence, while for non-deterministic automata it is ordinary bisimilarity. The powerset construction is a standard method for converting a nondeterministic automaton into an equivalent deterministic one as far as language is concerned. In this paper, we lift the powerset construction on automata to the more general framework of coalgebras with structured state spaces. Examples of applications include partial Mealy machines, (structured) Moore automata, and Rabin probabilistic automata.

Verification of a Timed Multitask System With Uppaal

Abstract: System and program verification has been a large area of research since the introduction of computers in industrial systems. It is an especially important issue for critical systems, where errors can cause human and financial damages. Programmable Logic Controllers (PLCs) are now widely used in many industrial systems and verification of the corresponding programs has already been studied in various contexts for a few years, for the benefit of users and system designers. First restricted to an untimed setting, verification was recently extended to systems where quantitative constraints are needed, possibly related to time elapsing. For instance, timed features like TON (Timers ON delay), used in PLC programs, were modeled with timed automata, thus increasing the size of the verification problems addressed. In this framework, we propose the modeling and verification of a particular timed multitask PLC program, which is part of the so-called MSS (Mecatronic Standard System) platform from Bosch Group. In this case study, time aspects are combined with multitask programming, which raises questions related to the reaction time between the detection of a signal and the resulting event. Our model for station 2 of the MSS platform is a network of timed automata, including automata for the operative part and for the control program, which is first described in SFC then translated in Ladder Diagram. This model is constrained with atomicity hypotheses concerning program execution, and model checking of a reaction time property is performed with the tool UPPAAL.

Recursive timed automata

Abstract: We study recursive timed automata that extend timed automata with recursion. Timed automata, as introduced by Alur and Dill, are finite automata accompanied by a finite set of real-valued variables called clocks. Recursive timed automata are finite collections of timed automata extended with special states that correspond to (potentially recursive) invocations of other timed automata from their collection. During an invocation of a timed automaton, our model permits passing the values of clocks using both pass-byvalue and pass-by-reference mechanisms. We study the natural reachability and termination (reachability with empty invocation stack) problems for recursive timed automata. We show that these problems are decidable (in many cases with the same complexity as the reachability problem on timed automata) for recursive timed automata satisfying the following condition: during each invocation either all clocks are passed by reference or none is passed by reference. Furthermore, we show that for recursive timed automata that violate this condition reachability/termination problems are undecidable for automata with as few as three clocks. We also establish similar results for two-player game extension of our model against reachability/termination objective.

Supervisory Control Synthesis of Discrete-Event Systems using Coordination Scheme

Abstract: Supervisory control of distributed DES with a global specification and local supervisors is a difficult problem. For global specifications, the equivalent conditions for local control synthesis to equal global control synthesis may not be met. This paper formulates and solves a control synthesis problem for a generator with a global specification and with a combination of a coordinator and local controllers. Conditional controllability is proven to be an equivalent condition for the existence of such a coordinated controller. A procedure to compute the least restrictive solution within our coordination control architecture is provided and conditions under which the result coincides with the supremal controllable sublanguage are stated.

Optimal path planning under temporal logic constraints

Abstract: In this paper we present a method for automatically generating optimal robot trajectories satisfying high level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by a general linear temporal logic formula. In addition, we require that an optimizing proposition must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot trajectory which minimizes the cost function. The problem is motivated by robotic monitoring and data gathering. In this setting, the optimizing proposition is satisfied at locations where data can be uploaded, and the formula specifies a an infinite horizon data collection mission. Our method utilizes Buchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal logic formula. We then present a graph algorithm which computes a path corresponding to the optimal robot trajectory. We also present an implementation for a robot performing a data gathering mission.

Model checking succinct and parametric one-counter automata

Abstract: We investigate the decidability and complexity of various model checking problems over one-counter automata. More specifically, we consider succinct one-counter automata, in which additive updates are encoded in binary, as well as parametric one-counter automata, in which additive updates may be given as unspecified parameters. We fully determine the complexity of model checking these automata against CTL, LTL, and modal µ-calculus specifications.

Beyond Hyper-Minimisation--Minimising DBAs and DPAs is NP-Complete

Abstract: In this paper we study the problem of minimising deterministic automata over finite and infinite words. Deterministic finite automata are the simplest devices to recognise regular languages, and deterministic \buchi, \cobuchi, and parity automata play a similar role in the recognition of $\omega$-regular languages. While it is well known that the minimisation of deterministic finite and weak automata is cheap, the complexity of minimising deterministic \buchi\ and parity automata has remained an open challenge. We establish the NP-completeness of these problems. A second contribution of this paper is the introduction of almost equivalence, an equivalence class for strictly between language equivalence for deterministic \buchi\ or \cobuchi\ automata and language equivalence for deterministic finite automata. Two finite automata are almost equivalent if they, when used as a monitor, provide a different answer only a bounded number of times in any run, and we call the minimal such automaton relatively minimal. Minimisation of DFAs, hyper-minimisation, relative minimisation, and the minimisation of deterministic \buchi\ (or \cobuchi) automata are operations of increasing reduction power, as the respective equivalence relations on automata become coarser from left to right. Besides being a natural equivalence relation for finite automata, almost equivalence is language preserving for weak automata, and can therefore also be viewed as a generalisation of language equivalence for weak automata to a more general class of automata. From the perspective of \buchi\ and \cobuchi\ automata, we gain a cheap algorithm for state-space reduction that also turns out to be beneficial for further heuristic or exhaustive state-space reductions put on top of it.

Finite-memory automata with non-deterministic reassignment

Abstract: In this paper we extend finite-memory automata with non-deterministic reassignment that allows an automaton to "guess" the future content of its registers, and introduce the corresponding notion of a regular expression over an infinite alphabet.

A Fuzzy Petri-Nets Model for Computing With Words

Abstract: Motivated by Zadeh's paradigm of computing with words (CWs) rather than numbers, several formal models of CWs have recently been proposed. These models are based on automata and, thus, are not well suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, which is called the Petri net, together with fuzzy-set theory and, thereby, establish a concurrency model of CWs-fuzzy Petri nets for CWs (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW that makes computing with more words possible. The language expressiveness of the two formal models of CWs, i.e., fuzzy automata for CWs as well as FPNCWs, is compared. A few small examples are provided to illustrate the theoretical development.

Minimization of Automata

Abstract: This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text processing, image analysis, linguistic computer science, and many other applications. There are two main families of minimization algorithms. The first by a sequence of refinements of a partition of the set of states, the second by a sequence of fusions or merges of states. Hopcroft's and Moore's algorithms belong to the first family, the linear-time minimization of acyclic automata of Revuz belongs to the second family. One of our studies is upon the comparison of the nature of Moore's and Hopcroft's algorithms. This gives some new insight in both algorithms. As we shall see, these algorithms are quite different both in behavior and in complexity. In particular, we show that it is not possible to simulate the computations of one of the algorithm by the other. We describe the minimization algorithm by fusion for so-called local automata. A special case of minimization is the construction o minimal automata for finite sets. We consider briefly this case, and in particular describe incremental algorithms. Finally, we consider the case of updating a minimal automaton when a word is added or removed from the set it recognizes.

An Extension of Data Automata that Captures XPath

Abstract: We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer decidability and expressibility questions for XPath. Finally, we use the newly introduced automata as a common framework to classify existing automata on data words and trees, including data automata, register automata and alternating register automata.

Choice functions and well-orderings over the infinite binary tree

Abstract: We give a new proof showing that it is not possible to define in monadic second-order logic (MSO) a choice function on the infinite binary tree. This result was first obtained by Gurevich and Shelah using set theoretical arguments. Our proof is much simpler and only uses basic tools from automata theory. We show how the result can be used to prove the inherent ambiguity of languages of infinite trees. In a second part we strengthen the result of the non-existence of an MSO-definable well-founded order on the infinite binary tree by showing that every infinite binary tree with a well-founded order has an undecidable MSO-theory.