Showing papers on "Automata theory published in 2004"

Finite state machines for strings over infinite alphabets

Abstract: Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of automaton we consider one-way and two-way variants, as well as deterministic, nondeterministic, and alternating control. We investigate the expressiveness and complexity of the automata and their connection to the logics, as well as standard decision problems. Some of our results answer open questions of Kaminski and Francez on register automata.

Optimal paths in weighted timed automata

Abstract: We consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-teachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)| + |W max |)), where n is the number of clocks, |δ(A)| is the size of the clock constraints and |W max | is the size of the largest weight. We show that this algorithm can be improved, if we restrict to weighted timed automata with a single clock. In case we consider a single starting state for the optimal-reachability problem, our approach yields an algorithm that takes exponential time only in the length of clock constraints.

Networks of Learning Automata

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A mathematical framework for cellular learning automata

Abstract: The cellular learning automata, which is a combination of cellular automata, and learning automata, is a new recently introduced model. This model is superior to cellular automata because of its ability to learn and is also superior to a single learning automaton because it is a collection of learning automata which can interact with each other. The basic idea of cellular learning automata, which is a subclass of stochastic cellular learning automata, is to use the learning automata to adjust the state transition probability of stochastic cellular automata. In this paper, we first provide a mathematical framework for cellular learning automata and then study its convergence behavior. It is shown that for a class of rules, called commutative rules, the cellular learning automata converges to a stable and compatible configuration. The numerical results also confirm the theoretical investigations.

SPOT: an extensible model checking library using transition-based generalized Bu/spl uml/chi automata

Abstract: SPOT (SPOT produces our traces), is a C++ library offering model checking bricks that can be combined and interfaced with third party tools to build a model checker It relies on transition-based generalized Bu/spl uml/chi automata (TGBA) and does not need to degeneralize these automata to check their emptiness We motivate the choice of TGBA by illustrating a very simple (yet efficient) translation of LTL (linear temporal logic) into TGBA We then show how it supports on-the-fly computations, and how it can be extended or integrated in other tools

On the language inclusion problem for timed automata: closing a decidability gap

Abstract: We consider the language inclusion problem for timed automata: given two timed automata A and B, are all the timed traces accepted by B also accepted by A? While this problem is known to be undecidable, we show here that it becomes decidable if A is restricted to having at most one clock. This is somewhat surprising, since it is well-known that there exist timed automata with a single clock that cannot be complemented. The crux of our proof consists in reducing the language inclusion problem to a reachability question on an infinite graph; we then construct a suitable well-quasi-order on the nodes of this graph, which ensures the termination of our search algorithm. We also show that the language inclusion problem is decidable if the only constant appearing among the clock constraints of A is zero. Moreover, these two cases are essentially the only decidable instances of language inclusion, in terms of restricting the various resources of timed automata.

PAC-learnability of Probabilistic Deterministic Finite State Automata

Abstract: We study the learnability of Probabilistic Deterministic Finite State Automata under a modified PAC-learning criterion We argue that it is necessary to add additional parameters to the sample complexity polynomial, namely a bound on the expected length of strings generated from any state, and a bound on the distinguishability between states With this, we demonstrate that the class of PDFAs is PAC-learnable using a variant of a standard state-merging algorithm and the Kullback-Leibler divergence as error function

Recursive data mining for masquerade detection and author identification

Abstract: In this paper, a novel recursive data mining method based on the simple but powerful model of cognition called a conceptor is introduced and applied to computer security. The method recursively mines a string of symbols by finding frequent patterns, encoding them with unique symbols and rewriting the string using this new coding. We apply this technique to two related but important problems in computer security: (i) masquerade detection to prevent a security attack in which an intruder impersonates a legitimate user to gain access to the resources, and (ii) author identification, in which anonymous or disputed computer session needs to be attributed to one of a set of potential authors. Many methods based on automata theory, hidden Markov models, Bayesian models or even matching algorithms from bioinformatics have been proposed to solve the masquerading detection problem but less work has been done on the author identification. We used recursive data mining to characterize the structure and high-level symbols in user signatures and the monitored sessions. We used one-class SVM to measure the similarity of these two characterizations. We applied weighting prediction scheme to author identification. On the SEA dataset that we used in our experiments, the results were very promising.

Hybrid systems modeling for power systems

Abstract: In this work a framework for modeling power systems using hybrid input/output automata (HIOA) is proposed. The system is assumed to consist of several distinct components. Some of them drive the continuous dynamics while others exhibit event-driven discrete dynamics. Such behavior is characterized by interactions between continuous dynamics and discrete events. Therefore the power systems are an important example of hybrid systems. This hybrid modeling process is applied to a simple power system.

Automata theory based on quantum logic: some characterizations

Abstract: Automata theory based on quantum logic (abbr l-valued automata theory) may be viewed as a logical approach of quantum computation In this paper, we characterize some fundamental properties of l-valued automata theory, and discover that some properties of the truth-value lattices of the underlying logic are equivalent to certain properties of automata More specifically (i) the transition relations of l-valued automata are extended to describe the transitions enabled by strings of input symbols, and particularly, these extensions depend on the distributivity of the truth-value lattices (Proposition 31); (ii) some properties of the l-valued successor and source operators and l-valued subautomata are demonstrated to be equivalent to a property of the truth-value lattices which is exactly equivalent to the distributive law (Proposition 43 and Corollary 44) This is a new characterization of Boolean algebras in the framework of l-valued automata theory; (iii) we verify that the intersection of two l-valued subautomata is still an l-valued subautomaton if and only if the multiplication (&) is distributive over the union in the truth-value lattices (Proposition 45), which is strictly weaker than the usual distributivity; (iv) we show that some topological characterizations in terms of the l-valued successor and source operators also rely on the distributivity of truth-value lattices (Theorem 56) Finally, we address some related topics for further study

Models and temporal logics for timed component connectors

Abstract: The coordination language Reo supports compositional system construction through connectors with real-time properties that exogenously coordinate the interactions among the constituent components into a coherent collaboration In this paper, we present an operational semantics for the channel-based component connectors of Reo in terms of Timed Constraint Automata and introduce a temporal-logic for specification and verification of their real-time properties

Vector addition tree automata

Abstract: We introduce a new class of automata, which we call vector addition tree automata. These automata are a natural generalization of vector addition systems with states, which are themselves equivalent to Petri-nets. Then, we prove that the decidability of provability in multiplicative exponential linear logic (which is an open problem) is equivalent to the decidability of the reachability relation for vector addition tree automata. This result generalizes the well-known connection existing between Petri nets and the !-horn fragment of multiplicative exponential linear logic.

Visual timed event scenarios

Abstract: Formal description of real-time requirements is a difficult and error prone task. Conceptual and tool support for this activity plays a central role in the agenda of technology transference from the formal verification engineering community to the real-time systems development practice. In this article we present VTS, a visual language to define complex event-based requirements such as freshness, bounded response, event correlation, etc. The underlying formalism is based on partial orders and supports real-time constraints. The problem of checking whether a timed automaton model of a system satisfies these sort of scenarios is shown to be decidable. Moreover, we have also developed a tool that translates visually specified scenarios into observer timed automata. The resulting automata can be composed with a model under analysis in order to check satisfaction of the stated scenarios. We show the benefits of applying these ideas to some case studies.

Assume-guarantee reasoning for hybrid I/O-automata by over-approximation of continuous interaction

Abstract: Assume-guarantee reasoning (AGR) is recognized as a means to counter the state explosion problem in the verification of safety properties. We propose a novel assume-guarantee rule for hybrid systems based on simulation relations. This makes it possible to perform compositional reasoning that is conservative in the sense of over-approximating the composed behaviors. The framework is formally based on hybrid input/output automata and their labeled transition system semantics. In contrast to previous approaches that require global receptivity conditions, the circularity is broken in our approach by a state-based nonblocking condition that can be checked in the course of computing the AGR simulation relations. The proposed procedures for AGR are implemented in a computational tool, called PHAVer, for the class of linear hybrid I/O automata, and the approach is illustrated with a simple example.

On deterministic finite automata and syntactic monoid size

Abstract: We investigate the relationship between regular languages and syntactic monoid size. In particular, we consider the transformation monoids of n-state (minimal) deterministic finite automata. We show tight upper and lower bounds on the syntactic monoid size depending on the number of generators (input alphabet size) used. It turns out, that the two generator case is the most involved one. There we show a lower bound of nn (1 - 2/√n) for the size of the syntactic monoid of a language accepted by an n-state deterministic finite automaton with binary input alphabet. Moreover, we prove that for every prime n ≥ 7, the maximal size semigroup w.r.t. its size among all (transformation) semigroups which can be generated with two generators, is generated by a permutation with two cycles (of appropriate lengths) and a non-bijective mapping merging elements from these two cycles. As a by-product of our investigations we determine the maximal size among all semigroups generated by two transformations, where one is a permutation with a single cycle and the other is a non-bijective mapping.

DP Lower bounds for equivalence-checking and model-checking of one-counter automata

Abstract: We present a general method for proving DP-hardness of problems related to formal verification of one-counter automata. For this we show a reduction of the SAT-UNSAT problem to the truth problem for a fragment of (Presburger) arithmetic. The fragment contains only special formulas with one free variable, and is particularly apt for transforming to simulation-like equivalences on one-counter automata. In this way we show that the membership problem for any relation subsuming bisimilarity and subsumed by simulation preorder is DP-hard (even) for one-counter nets (where the counter cannot be tested for zero). We also show DP-hardness for deciding simulation between one-counter automata and finite-state systems (in both directions), and for the model-checking problem with one-counter nets and the branching-time temporal logic EF.

Asynchronous automata networks can emulate any synchronous automata network

Abstract: We show that any locally finite automata network with global synchronous updates can be emulated by another one , whose structure derives from that of by a simple construction, but whose updates are made asynchronously at its various component automata (e.g. possibly randomly or sequentially, with or without possible simultaneous updates at different nodes). By "emulation", we refer to the existence of a spatial-temporal covering 'local time', allowing one to project the behavior of continuously onto that of . We also show the existence of a spatial-temporal section of the asynchronous automata network's behavior which completely determines the synchronous global state of at every time step. We give the construction of the asynchronous automata network, establish its freedom from deadlocks, and construct local time functions and spatial-temporal sections relating any posssible behavior of to the single corresponding behavior of on a given input sequence starting from a given initial global state. This establishes that the behavior of any locally finite synchronous automata network actually can be emulated without the restriction of synchronous update, freeing us from the need of a global clock signal. Local information is sufficient to guarantee that the synchronous behavior of is completely determined by any asynchronous behavior of starting from a corresponding global state and given the same input sequence as . Moreover, the relative passage of corresponding local time at any two nodes in is bounded in a simple way by approximately one-third of the distance between them. As corollaries, any synchronous generalized cellular automaton or synchronous cellular automaton can be emulated by an asynchronous one of the same type. Implementation aspects of these asynchronous automata are also discussed, and open problems and research directions are indicated.

A CLP proof method for timed automata

Abstract: Constraint logic programming (CLP) has been used to model programs and transition systems for the purpose of verification problems. In particular, it has been used to model timed safety automata (TSA). In this paper, we start with a systematic translation of TSA into CLP. The main contribution is an expressive assertion language and a CLP inference method for proving assertions. A distinction of the assertion language is that it can specify important properties beyond traditional safety properties. We highlight one important property: that a system of processes is symmetric. The inference mechanism is based upon the well-known method of tabling in logic programming. It is distinguished by its ability to use assertions that are not yet proven, using a principle of coinduction. Apart from given assertions, the proof mechanism can also prove implicit assertions such as discovering a lower or upper bound of a variable. Finally, we demonstrate significant improvements over state-of-the-art systems using standard TSA benchmark examples.

Global model-checking of infinite-state systems

Abstract: In this paper we extend the automata-theoretic framework for reasoning about infinite-state sequential systems to handle also the global model-checking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by a two-way automaton that navigates through the tree. The framework is known for local model checking. For branching time properties, the framework uses two-way alternating automata. For linear time properties, the framework uses two-way path automata. In order to solve the global model-checking problem we show that for both types of automata, given a regular tree, we can construct a nondeterministic word automaton that accepts all the nodes in the tree from which an accepting run of the automaton can start.

Algebraic theory of automata and languages

Abstract: Although there are some books dealing with algebraic theory of automata, their contents consist mainly of Krohn-Rhodes theory and related topics. The topics in the present book are rather different. For example, automorphism groups of automata and the partially ordered sets of automata are systematically discussed. Moreover, some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with. The book is self-contained and hence does not require any knowledge of automata and formal languages.

Algebraic Recognizability of Languages

Abstract: Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.

A translation based method for the timed analysis of scheduling extended time Petri nets

Abstract: In this paper, we present a method for the timed analysis of real-time systems, taking into account the scheduling constraints. The model considered is an extension of time Petri nets, scheduling extended time Petri nets (SETPN) for which the valuations of transitions may be stopped and resumed, thus allowing the modelling of preemption. This model has a great expressivity and allows a very natural modelling. The method we propose consists of precomputing, with a fast algorithm, the state space of the SETPN as a stopwatch automaton (SWA). This stopwatch automaton is proven timed bisimilar to the SETPN, so we can perform the timed analysis of the SETPN through it with the tool on linear hybrid automata, HYTECH. The main interests of this precomputation are that it is fast because it is difference bounds matrix (DBM)-based, and that it has online stopwatch reduction mechanisms. Consequently, the resulting stopwatch automaton has, in the general case, a fairly lower number of stopwatches than what could be obtained by a direct modelling of the system as SWA. Since the number of stopwatches is critical for the complexity of the verification, the method increases the efficiency of the timed analysis of the system, and in some cases may just make it possible at all.