Showing papers on "ω-automaton published in 2004"
Book•
12 Feb 2004
TL;DR: The first manual devoted to Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words.
Abstract: Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of B chi, McNaughton and Sch tzenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.
337 citations
TL;DR: This work investigates the expressiveness and complexity of the automata and their connection to the logics, as well as standard decision problems of Kaminski and Francez on register automata.
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.
305 citations
109 citations
Journal Article•
TL;DR: It is demonstrated 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.
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
98 citations
01 Feb 2004
TL;DR: Detailed simulation results are presented that indicate that the proposed stochastic estimator scheme converges faster than the deterministic-estimator-based DP/sub RI/ and DGPA schemes when operating in stationary P-model random environments.
Abstract: A new class of P-model absorbing learning automata is introduced. The proposed automata are based on the use of a stochastic estimator in order to achieve a rapid and accurate convergence when operating in stationary random environments. According to the proposed stochastic estimator scheme, the estimates of the reward probabilities of actions are not strictly dependent on the environmental responses. The dependence between the stochastic estimates and the deterministic ones is more relaxed for actions that have been selected only a few times. In this way, actions that have been selected only a few times, have the opportunity to be estimated as "optimal," to increase their choice probability and consequently, to be selected. In this way, the estimates become more reliable and consequently, the automaton rapidly and accurately converges to the optimal action. The asymptotic behavior of the proposed scheme is analyzed and it is proved to be /spl epsi/-optimal in every stationary random environment. Furthermore, extensive simulation results are presented that indicate that the proposed stochastic estimator scheme converges faster than the deterministic-estimator-based DP/sub RI/ and DGPA schemes when operating in stationary P-model random environments.
53 citations
TL;DR: A class of fuzzy finite automata corresponding to the Mealy type of ordinary automata is formulated, and also two types of statewise equivalence relations are introduced.
50 citations
17 Jun 2004
TL;DR: It is shown that for a reading window of size one and nonrecursive DTDs with one-unambiguous content there is an algorithm producing a deterministic automaton that validates documents with respect to that DTD, and conditions under which they can be validated against by using one-counter automata are considered.
Abstract: We study validation of streamed XML documents by means of finite state machines. Previous work has shown that validation is in principle possible by finite state automata, but the construction was prohibitively expensive, giving an exponential-size nondeterministic automaton. Instead, we want to find deterministic automata for validating streamed documents: for them, the complexity of validation is constant per tag. We show that for a reading window of size one and nonrecursive DTDs with one-unambiguous content (i.e. conforming to the current XML standard) there is an algorithm producing a deterministic automaton that validates documents with respect to that DTD. The size of the automaton is at most exponential and we give matching lower bounds. To capture the possible advantages offered by reading windows of size k, we introduce k-unambiguity as a generalization of one-unambiguity, and study the validation against DTDs with k-unambiguous content. We also consider recursive DTDs and give conditions under which they can be validated against by using one-counter automata.
47 citations
TL;DR: An attempt has been made to characterise a number of exceptional transformations or rules, each of which behaving uniquely, not matching with any other rules, of two dimensional cellular automata with null and periodic boundary conditions.
46 citations
TL;DR: It is shown 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.
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.
42 citations
13 Jul 2004
TL;DR: The automata-theoretic framework for reasoning about infinite-state sequential systems is extended to handle also the global model-checking problem, and it is shown that for both types of automata, given a regular tree, it can construct a nondeterministic word automaton that accepts all the nodes in the tree from which an accepting run of the automaton can start.
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.
39 citations
02 Nov 2004
TL;DR: The time complexity of the minimization problem for two restricted types of finite automata is investigated and it is found that these automata are nearly deterministic, since they only allow a small amount of nondeterminism to be used.
Abstract: It is known that deterministic finite automata (DFAs) can be algorithmically minimized, i.e., a DFA M can be converted to an equivalent DFA M' which has a minimal number of states. The minimization can be done efficiently (in: Z. Kohavi (Ed.), Theory of Machines and Computations, Academic Press, New York, 1971, pp. 189-196). On the other hand, it is known that unambiguous finite automata and nondeterministic finite automata can be algorithmically minimized too, but their minimization problems turn out to be NP-complete and PSPACE-complete, respectively (SIAM J. Comput. 22(6) (1993) 1117-1141). In this paper, the time complexity of the minimization problem for two restricted types of finite automata is investigated. These automata are nearly deterministic, since they only allow a small amount of nondeterminism to be used. The main result is that the minimization problems for these models are computationally hard, namely NP-complete. Hence, even the slightest extension of the deterministic model towards a nondeterministic one, e.g., allowing at most one nondeterministic move in every accepting computation or allowing two initial states instead of one, results in computationally intractable minimization problems.
Book•
01 Jan 2004
TL;DR: Some operations on languages and special classes of regular languages associated with deterministic and nondeterministic directable automata are dealt with and automorphism groups of automata and the partially ordered sets of Automata are systematically discussed.
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.
13 Jul 2004
TL;DR: It is proved that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula.
Abstract: Automata provide an effective mechanization of decision procedures for Presburger arithmetic. However, only crude lower and upper bounds are known on the sizes of the automata produced by this approach. In this paper, we prove that the number of states of the minimal deterministic automaton for a Presburger arithmetic formula is triple exponentially bounded in the length of the formula. This upper bound is established by comparing the automata for Presburger arithmetic formulas with the formulas produced by a quantifier elimination method. We also show that this triple exponential bound is tight (even for nondeterministic automata). Moreover, we provide optimal automata constructions for linear equations and inequations.
Book•
01 Dec 2004
TL;DR: This paper presents a meta-analyses of Krohn-Rhodes theory and its applications to automata networks, aiming at determining the boundaries between state-homogeneous and asynchronous networks.
Abstract: Preface and overview 1. Preliminaries 2. Directed graphs, automata, and automata networks 3. Krohn-Rhodes theory and complete classes 4. Without Letichevsky's criterion 5. Letichevsky's criterion 6. Primitive products and temporal products 7. Finite state-homogeneous automata networks and asynchronous automata networks Bibliography Index.
Journal Article•
TL;DR: It is provided the basics of a 2-dimensional theory of automata on series-parallel biposets and relates these classes to languages of series-Parallel bipOSets definable in monadic second-order logic.
Abstract: We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.
TL;DR: It is proved that a group G has a word problem that is accepted by a deterministic counter automaton with a weak inverse property if and only if G is virtually abelian.
01 Dec 2004
TL;DR: This thesis considers minimality and size reduction issues of one-tape and multitape automata and shows that any bideterministic automaton is a unique minimal automaton among all NFA accepting its language.
Abstract: In this thesis, we consider minimality and size reduction issues of one-tape and multitape automata. Although the topic of minimization of one-tape automata has been widely studied for many years, it seems that some issues have not gained attention. One of these issues concerns finding specific conditions on automata that imply their minimality in the class of nondeterministic finite automata (NFA) accepting the same language. Using the theory of NFA minimization developed by Kameda and Weiner in 1970, we show that any bideterministic automaton (that is, a deterministic automaton with its reversal also being deterministic) is a unique minimal automaton among all NFA accepting its language. In addition to the minimality in regard to the number of states, we also show its minimality in the number of transitions. Using the same theory of Kameda and Weiner, we also obtain a more general minimality result. We specify a set of sufficient conditions under which a minimal deterministic automaton (DFA) accepting some language or the reversal of the minimal DFA of the reversal language is a minimal NFA of the language. We also consider multitape bideterministic automata and show by a counterexample that such automata are not necessarily minimal. However, given a set of accepting computations of a bideterministic multitape automaton, we show that this automaton is a unique minimal automaton with this set of accepting computations.
22 Aug 2004
TL;DR: A natural class of cellular automata characterised by a property of the local transition law without any assumption on the states set is introduced, and Rice's theorem for limit sets is no longer true for that class, although infinitely many properties of limit sets are still undecidable.
Abstract: We introduce a natural class of cellular automata characterised by a property of the local transition law without any assumption on the states set. We investigate some algebraic properties of the class and show that it contains intrinsically universal cellular automata. In addition we show that Rice’s theorem for limit sets is no longer true for that class, although infinitely many properties of limit sets are still undecidable.
TL;DR: This work defines q quantum pushdown automata (qQPDAs) and QPDAs that are at least as powerful as those defined by Moore and Crutchfield, and focuses on demonstrating the equivalence between qQPD as well as the properties of languages accepted by qZPDAs.
11 Oct 2004
TL;DR: In the setting of identification in the limit with probability one, it is proved that stochastic deterministic finite automata cannot be identified from only a polynomial quantity of data.
Abstract: Stochastic deterministic finite automata have been introduced and are used in a variety of settings. We report here a number of results concerning the learnability of these finite state machines. In the setting of identification in the limit with probability one, we prove that stochastic deterministic finite automata cannot be identified from only a polynomial quantity of data. If concerned with approximation results, they become Pac-learnable if the L ∞ norm is used. We also investigate queries that are sufficient for the class to be learnable.
20 Dec 2004
TL;DR: The decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ is looked at and applications to automated composition of e-services are identified.
Abstract: Let ${\mathcal M}$ be a class of (possibly nondeterministic) language acceptors with a one-way input tape A system (A; A1, ..., Ar) of automata in ${\mathcal M}$, is composable if for every string w = a1 .. an of symbols accepted by A, there is an assignment of each symbol in w to one of the Ai's such that if wi is the subsequence assigned to Ai, then wi is accepted by Ai For a nonnegative integer k, a k-lookahead delegator for (A; A1, ..., Ar) is a deterministic machine D in ${\mathcal M}$ which, knowing (a) the current states of A, A1, ..., Ar and the accessible “local” information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the k lookahead symbols to the right of the current input symbol being processed, can uniquely determine the Ai to assign the current symbol Moreover, every string w accepted by A is also accepted by D, i.e., the subsequence of string w delegated by D to each Ai is accepted by Ai Thus, k-lookahead delegation is a stronger requirement than composability, since the delegator D must be deterministic A system that is composable may not have a k-delegator for any k We look at the decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ Our results have applications to automated composition of e-services When e-services are modeled by automata whose alphabet represents a set of activities or tasks to be performed (namely, activity automata), automated design is the problem of “delegating” activities of the composite e-service to existing e-services so that each word accepted by the composite e-service can be accepted by those e-services collectively with each accepting a subsequence of the word, under possibly some Presburger constraints on the numbers and types of activities that can be delegated to the different e-services Our results generalize earlier ones (and resolve some open questions) concerning composability of deterministic finite automata as e-services to finite automata that are augmented with unbounded storage (e.g., counters and pushdown stacks) and finite automata with discrete clocks (i.e., discrete timed automata) We look at the decidability of composability and existence of k-delegators for various classes of machines ${\mathcal M}$ Our results have applications to automated composition of e-services E-services provide a general framework for discovery, flexible interoperation, and dynamic composition of distributed and heterogeneous processes on the Internet Automated composition allows a specified composite e-service to be implemented by composing existing e-services When e-services are modeled by automata whose alphabet represents a set of activities or tasks to be performed (namely, activity automata), automated design is the problem of “delegating” activities of the composite e-service to existing e-services so that each word accepted by the composite e-service can be accepted by those e-services collectively with each accepting a subsequence of the word, under possibly some Presburger constraints on the numbers and types of activities that can be delegated to the different e-services Our results generalize earlier ones (and resolve some open questions) concerning composability of deterministic finite automata as e-services to finite automata that are augmented with unbounded storage (e.g., counters and pushdown stacks) and finite automata with discrete clocks (i.e., discrete timed automata).
01 Jan 2004
TL;DR: An algorithm for generating deterministic finite state machine approximations of stable, discrete time, first order LTI systems with finite input alphabets and quantized outputs is proposed.
Abstract: We consider stable, discrete time, first order LTI systems with finite input alphabets and quantized outputs. We propose an algorithm for generating deterministic finite state machine approximations of these systems with computable bounds on approximation error, and we describe the conditions under which the bounds are valid.
TL;DR: It is shown that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
Abstract: In this article we generalize concepts of the position automaton and ZPC-structure to the regular -expressions. We show that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.
01 Mar 2004
TL;DR: Language Emulator introduces error-detecting and internationalization functionalities into automata tools in order to help undergraduate students to understand the concepts of Automata Theory.
Abstract: Language Emulator, written in Java, is a toolkit to help undergraduate students to understand the concepts of Automata Theory. The software allows the manipulation of regular expressions, regular grammars, deterministic finite automata, nondeterministic finite automata with and without lambda transitions, and Moore and Mealy machines. Language Emulator introduces error-detecting and internationalization functionalities into automata tools. It has been accepted by 95% of students in a recent survey, indicating that it is a helpful toolkit in learning Automata Theory.
22 Jul 2004
TL;DR: It is proved that deterministic expression automata languages are a proper subfamily of the regular languages and the minimization of deterministicexpression automata is defined.
Abstract: We explore expression automata with respect to determinism, minimization and primeness. We define determinism of expression automata using prefix-freeness. This approach is, to some extent, similar to that of Giammarresi and Montalbano’s definition of deterministic generalized automata. We prove that deterministic expression automata languages are a proper subfamily of the regular languages. We define the minimization of deterministic expression automata. Lastly, we discuss prime prefix-free regular languages.
Note that we have omitted almost all proofs in this preliminary version.
Journal Article•
TL;DR: A new model of weighted automata is introduced and the decidability of its limitedness problem is shown by solving the underlying Burnside problem.
Abstract: We give a positive solution to the so-called finite substitution problem which was open for more than 10 years [11]: given recognizable languages K and L, decide whether there exists a finite substitution σ such that σ(K) = L. For this, we introduce a new model of weighted automata and show the decidability of its limitedness problem by solving the underlying Burnside problem.
05 Jul 2004
TL;DR: The net effect is that of obtaining a lighter automaton than the directed acyclic word graph (DAWG) of Blumer et al., as it uses less nodes, still with arcs labeled by single characters.
Abstract: We describe a new technique for reducing the number of nodes and symbols in automata based on tries. The technique stems from some results on anti-dictionaries for data compression and does not need to retain the input string, differently from other methods based on compact automata. The net effect is that of obtaining a lighter automaton than the directed acyclic word graph (DAWG) of Blumer et al., as it uses less nodes, still with arcs labeled by single characters.
Journal Article•
TL;DR: A method for determining multilinear state space models for general finite state automata is presented and the cyclic structure of the state space is shown to be determined only by the periods of the elementary divisor polynomials of the system dynamics.
01 Jan 2004
TL;DR: A generic method for deciding semantic equivalences between pushdown automata and finite-state automata, and special attention is devoted to bisimulation-like equivalences (including weak, early, delay, branching, and probabilistic bisimilarity).
Abstract: We propose a generic method for deciding semantic equivalences between pushdown automata and finite-state automata. The abstract part of the method is applicable to every process equivalence which is a right PDA congruence. Practical usability of the method is demonstrated on selected equivalences which are conceptual representatives of the whole spectrum. In particular, special attention is devoted to bisimulation-like equivalences (including weak, early, delay, branching, and probabilistic bisimilarity), and it is also shown how the method applies to simulation-like and trace-like equivalences. The generality does not lead to the loss of efficiency; the algorithms obtained by applying our method are essentially time-optimal and sometimes even polynomial. The list of particular results obtained by our method includes items which are first of their kind.