Showing papers on "ω-automaton published in 2002"
20 Aug 2002
TL;DR: In this article, the authors define and provide algorithms for computing a hierarchy of simulation relations on the state-spaces of ordinary transition systems, finite automata, and Buchi automata.
Abstract: We define and provide algorithms for computing a natural hierarchy of simulation relations on the state-spaces of ordinary transition systems, finite automata, and Buchi automata.T hese simulations enrich ordinary simulation and can be used to obtain greater reduction in the size of automata by computing the automaton quotient with respect to their underlying equivalence.Sta te reduction for Buchi automata is useful for making explicit-state model checking run faster ([EH00, SB00, EWS01]).We define k-simulations, where 1-simulation corresponds to ordinary simulation and its variants for Buchi automata ([HKR97, EWS01]), and k-simulations, for k > 1, generalize the game definition of 1-simulation by allowing the Duplicator to use k pebbles instead of 1 (to "hedge its bets") in response to the Spoiler's move of a single pebble.As k increases, ksimulations are monotonically non-decreasing relations. Indeed, when k reaches n, the number of states of the automaton, the n-simulations defined for finite-automata and for labeled transition systems correspond precisely to language containment and trace containment, respectively. But for each fixed k, the maximal k-simulation relation is computable in polynomial time: nO(k).This provides a mechanism with which to trade off increased computing time for larger simulation relation size, and more potential reduction in automaton size.W e provide algorithms for computing k-simulations using a natural generalization of a prior efficient algorithm based on parity games ([EWS01]) for computing various simulations.Lastly, we observe the relationship between k-simulations and a k-variable interpretation of modal logic.
210 citations
TL;DR: The 2-way quantum finite automata with quantum and classical states (2qcfa's) model as discussed by the authors is a variant of the classical 2qfa model, which may be simpler to implement than unrestricted 2qFa's; the internal state of a 2Qcfa may include a quantum part that may be in a mixed quantum state, but the tape head position is required to be classical.
182 citations
TL;DR: This paper characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group and shows that piecewise testable sets can be accepted with boundederror by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.
Abstract: The 2-way quantum finite automaton introduced by Kondacs and Watrous [Proceedings of the 38th Annual Symposium on Foundations of Computer Science, 1997, IEEE Computer Society, pp. 66--75] can accept nonregular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1-way quantum finite automaton is reduced to a proper subset of the regular languages.
In this paper we study two different models of 1-way quantum finite automata. The first model, termed measure-once quantum finite automata, was introduced by Moore and Crutchfield [ Theoret. Comput. Sci., 237 (2000), pp. 275--306], and the second model, termed measure-many quantum finite automata, was introduced by Kondacs and Watrous [Proceedings of the38th Annual Symposium on Foundations of Computer Science, 1997, IEEE Computer Society, pp. 66--75].
We characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group. We also show that it can be simulated by a probabilistic finite automaton and describe an algorithm that determines if two measure-once automata are equivalent.
We prove several closure properties of the classes of languages accepted by measure-many automata, including inverse homomorphisms, and provide a new necessary condition for a language to be accepted by the measure-many model with bounded error. Finally, we show that piecewise testable sets can be accepted with bounded error by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.
171 citations
22 Sep 2002
TL;DR: This work surveys some recent developments in the broad area of automata and logic which are motivated by the advent of XML, and considers unranked tree automata, tree-walking Automata, and automata over infinite alphabets.
Abstract: We survey some recent developments in the broad area of automata and logic which are motivated by the advent of XML. In particular, we consider unranked tree automata, tree-walking automata, and automata over infinite alphabets. We focus on their connection with logic and on questions imposed by XML.
168 citations
11 Nov 2002
TL;DR: This paper describes how, by labeling automata transitions rather than states, the size of automata generated by existing tableau-based translation algorithms is significantly reduced.
Abstract: Model checking is an automated technique for checking that a system satisfies a set of required properties. With explicit-state model checkers, properties are typically defined in linear-time temporal logic (LTL), and are translated into Buchi automata in order to be checked. This paper describes how, by labeling automata transitions rather than states, we significantly reduce the size of automata generated by existing tableau-based translation algorithms. Our optimizations apply to the core of the translation process, where generalized Buchi automata are constructed. These automata are subsequently transformed in a single efficient step into Buchi automata as used by model checkers. The tool that implements the work described here is released as part of the Java Path-Finder software (JPF), an explicit state model checker of Java programs under development at the NASA Ames Research Center.
143 citations
TL;DR: A new kind of fuzzy automata is introduced whose inputs are instead strings of fuzzy subsets of the input alphabet, indicating that computing with words can be implemented with computing with values with the price of a big amount of extra computations.
Abstract: Classical automata are formal models of computing with values. Fuzzy automata are generalizations of classical automata where the knowledge about the system's next state is vague or uncertain. It is worth noting that like classical automata, fuzzy automata can only process strings of input symbols. Therefore, such fuzzy automata are still (abstract) devices for computing with values, although a certain vagueness or uncertainty are involved in the process of computation. We introduce a new kind of fuzzy automata whose inputs are instead strings of fuzzy subsets of the input alphabet. These new fuzzy automata may serve as formal models of computing with words. We establish an extension principle from computing with values to computing with words. This principle indicates that computing with words can be implemented with computing with values with the price of a big amount of extra computations.
122 citations
TL;DR: The aim is to establish a theoretical relation between two well-known automata recognizing the language of E, namely the position automaton PE constructed by Glushkov or McNaughton and Yamada, and the equation automaton EE constructed by Mirkin or Antimirov.
98 citations
08 Apr 2002
TL;DR: This paper shows how the problem of job-shop scheduling where the jobs are preemptible can be modeled naturally as a shortest path problem defined on an extension of timed automata, namely stopwatch automata where some of the clocks might be freezed at certain states.
Abstract: In this paper we show how the problem of job-shop scheduling where the jobs are preemptible can be modeled naturally as a shortest path problem defined on an extension of timed automata, namely stopwatch automata where some of the clocks might be freezed at certain states. Although general verification problems on stopwatch automata are known to be undecidable, we show that due to particular properties of optimal schedules, the shortest path in the automaton belongs to a finite subset of the set of acyclic paths and hence the problem is solvable. We present several algorithms and heuristics for finding the shortest paths in such automata and test their implementation on numerous benchmark examples.
83 citations
08 Jul 2002
TL;DR: A new one-dimensional universal automaton with von Neumann neighborhood and only 6 states is constructed, thus improving the best known lower bound both for computational and intrinsic universality.
Abstract: We formalize the idea of intrinsically universal cellular automata, which is strictly stronger than classical computational universality. Thanks to this uniform notion, we construct a new one-dimensional universal automaton with von Neumann neighborhood and only 6 states, thus improving the best known lower bound both for computational and intrinsic universality.
66 citations
Journal Article•
TL;DR: This work gives asymptotic estimates and some explicit computations for both the number of distinct languages and theNumber of distinct finite languages over a k-letter alphabet that are accepted by deterministic finite automata with n states.
Abstract: We give asymptotic estimates and some explicit computations for both the number of distinct languages and the number of distinct finite languages over a k-letter alphabet that are accepted by deterministic finite automata (resp. nondeterministic finite automata) with n states.
65 citations
TL;DR: This paper introduces a new framework called “graph automata” to obtain a natural description of complicated spatio-temporal developmental processes such as self-reproduction and provides a new tool to approach important scientific problems such as evolution of morphology.
TL;DR: This article describes a simple and equally efficient method for modifying any minimal finite-state automaton (be it acyclic or not) so that a string is added to or removed from the language it accepts; both operations are very important when dictionary maintenance is performed.
Abstract: Daciuk et al. [Computational Linguistics 26(1):3-16 (2000)] describe a method for constructing incrementally minimal, deterministic, acyclic finite-state automata (dictionaries) from sets of strings. But acyclic finite-state automata have limitations: For instance, if one wants a linguistic application to accept all possible integer numbers or Internet addresses, the corresponding finite-state automaton has to be cyclic. In this article, we describe a simple and equally efficient method for modifying any minimal finite-state automaton (be it acyclic or not) so that a string is added to or removed from the language it accepts; both operations are very important when dictionary maintenance is performed and solve the dictionary construction problem addressed by Daciuk et al. as a special case. The algorithms proposed here may be straightforwardly derived from the customary textbook constructions for the intersection and the complementation of finite-state automata; the algorithms exploit the special properties of the automata resulting from the intersection operation when one of the finite-state automata accepts a single string.
Journal Article•
TL;DR: It is argued that if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of Automata theory rather then searching for new applications and defining numerous questionable modifications of basic models.
Abstract: "Automata theory is not over" is the message of this paper. But if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of automata theory rather then searching for new applications and defining numerous questionable modifications of basic models. We argue for this opinion here and try co outline a way that could lead to a renaissance of automata theory.
TL;DR: An accepting device based on the communication between finite automata working in parallel is introduced andHomomorphical characterizations of recursively enumerable languages are obtained starting from languages recognized by all variants of parallel communicating finite Automata systems having at most three components.
Abstract: An accepting device based on the communication between finite automata working in parallel is introduced. It consists of several finite automata working independently but communicating states to each other by request. Several variants of parallel communicating finite automata systems are investigated from their computational power point of view. We prove that all of them are at most as powerful as multi-head finite automata. Homomorphical characterizations of recursively enumerable languages are obtained starting from languages recognized by all variants of parallel communicating finite automata systems having at most three components. We present a brief comparison with the parallel communicating grammar systems. Some remarks suggesting that these devices might be mildly context-sensitive ones as well as a few open problems and directions for further research are also discussed.
TL;DR: Fuzzy automata offer new mechanisms for classification of classical automata and can be used for insight into their qualitative behavior as well as investigating their Boolean counterparts empirically and using rule entropy and repeated input response functions.
Abstract: Boolean cellular automata may be generalized to fuzzy automata in a consistent manner. Several fuzzy logics are used to create 1-dimensional automata and also 2-dimensional automata that generalize the game of life. These generalized automata are investigated and compared to their Boolean counterparts empirically and using rule entropy and repeated input response functions. Fuzzy automata offer new mechanisms for classification of classical automata and can be used for insight into their qualitative behavior. © 2002 Wiley Periodicals, Inc.
Journal Article•
TL;DR: In this article, the largest right-invariant equivalence on the states and then merge the states in the same class to obtain a smaller automaton is computed and applied to position automata.
Abstract: We give new methods for constructing small nondeterministic finite automata (NFA) from regular expressions or from other NFAs. Given an arbitrary NFA, we compute the largest right-invariant equivalence on the states and then merge the states in the same class to obtain a smaller automaton. When applying this method to position automata, we get a way to convert regular expressions into NFAs which can be arbitrarily smaller than the position, partial derivative, and follow automata. In most cases, it is smaller than all NFAs obtained by similar constructions.
08 Jul 2002
TL;DR: This paper gives in this paper a method to compute a reversible automaton from the minimal automaton of a reversible language that contains an equivalent automaton which is quasi-reversible.
Abstract: Reversible languages occur in many different domains Although the decision for the membership of reversible languages was solved in 1992 by Pin, an effective construction of a reversible automaton for a reversible language was still unknown We give in this paper a method to compute a reversible automaton from the minimal automaton of a reversible language With this intention, we use the universal automaton of the language that can be obtained from the minimal automaton and that contains an equivalent automaton which is quasi-reversible This quasi-reversible automaton has nearly the same properties as a reversible one and can easily be turned into a reversible automaton
TL;DR: The concept of cover automata for finite languages was formally introduced in [3], and an algorithm was given to solve the inequality of the following type: For α ≥ 1, β ≥ 1 using LaSalle's inequality.
Abstract: The concept of cover automata for finite languages was formally introduced in [3]. Cover automata have been studied as an efficient representation of finite languages. In [3], an algorithm was give...
01 Jan 2002
TL;DR: A submitted manuscript is the version of the article upon submission and before peer-review as mentioned in this paper, while a published version is the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
15 Aug 2002
TL;DR: In this paper, a notion of probabilistic reversible automata (PRA) is introduced and a strong relationship between different possible models of PRA and corresponding models of quantum finite automata is found.
Abstract: To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.
12 Dec 2002
TL;DR: Two new quotients are suggested, namely minimax and semi-elective quotients, which are proved to preserve the recognized languages and show that computing them is not more difficult than computing quotients for nondeterministic Buchi automata.
Abstract: Quotienting by simulation equivalences is a well-established technique for reducing the size of nondeterministic Buchi automataWe adapt this technique to alternating Buchi automata To this end we suggest two new quotients, namely minimax and semi-elective quotients, prove that they preserve the recognized languages, and show that computing them is not more difficult than computing quotients for nondeterministic Buchi automata We explain the merits of of our quotienting procedures with respect to converting alternating Buchi automata into nondeterministic ones
TL;DR: Testing automata can accept the same stuttering-insensitive languages as (state-labelled) Buchi automata, and they have at most the same number of states, but are also more often deterministic.
22 Jul 2002
TL;DR: An algorithmic calculus of the reachability relations on clock values defined by timed automata is given, by computing unions, compositions and reflexive-transitive closure (star) of "atomic" relations.
Abstract: We give an algorithmic calculus of the reachability relations on clock values defined by timed automata. Our approach is a modular one, by computing unions, compositions and reflexive-transitive closure (star) of "atomic" relations. The essential tool is a new representation technique for n-clock relations - the 2n-automata - and our strategy is to show the closure under union, composition and star of the class of 2n-automata that represent reachability relations in timed automata.
01 Jan 2002
TL;DR: It is found that a large number of modular discrete-event system verification problems are also PSPACE-complete, even for prefix-closed cases, suggesting that while system decomposition by parallel composition could lead to significant space savings, it may not lead to sufficient time savings that would aid in the study of "large-scale" systems.
Abstract: Investigates issues related to the computational complexity of automata intersection problems. For several classes of problems, comparing the behavior of sets of interacting finite automata is found to be PSPACE-complete even in the case of automata accepting prefix-closed languages (equivalently, even when all states are marked). The paper uses these results to investigate the computational complexity of problems related to the verification of supervisory controllers for modular discrete-event systems. Modular discrete-event systems are sets of finite automata combined by the parallel composition operation. We find that a large number of modular discrete-event system verification problems are also PSPACE-complete, even for prefix-closed cases. These results suggest that while system decomposition by parallel composition could lead to significant space savings, it may not lead to sufficient time savings that would aid in the study of "large-scale" systems.
27 Jul 2002
TL;DR: An automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems and the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems is developed.
Abstract: We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. 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 an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems.We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.
03 Jul 2002
TL;DR: An on-line algorithm is described building the finite automaton that accepts all common subsequences of the given set of strings.
Abstract: Given a set of strings, a common subsequence of this set is a string that is a subsequence of each string in this set. We describe an on-line algorithm building the finite automaton that accepts all common subsequences of the given set of strings.
Journal Article•
TL;DR: In this paper, the authors develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems 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.
Abstract: We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. 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 an alternating two-way automaton that navigates through the tree. We introduce path automata on trees. The input to a path automaton is a tree, but the automaton cannot split to copies and it can read only a single path of the tree. In particular, two-way nondeterministic path automata enable exactly the type of navigation that is required in order to check linear properties of infinite-state sequential systems. We demonstrate the versatility of the automata-theoretic approach by solving several versions of the model-checking problem for LTL specifications and prefix-recognizable systems. Our algorithm is exponential in both the size of (the description of) the system and the size of the LTL specification, and we prove a matching lower bound. This is the first optimal algorithm for solving the LTL model-checking problem for prefix recognizable systems. Our framework also handles systems with regular labeling.
Journal Article•
TL;DR: In this article, two algorithms for constructing small non-deterministic finite automata (NFA) from regular expressions have been proposed, one of which constructs NFAs with e-moves (eNFA), which is smaller than all the other eNFAs obtained by similar constructions.
Abstract: We give two new algorithms for constructing small nondeterministic finite automata (NFA) from regular expressions. The first constructs NFAs with e-moves (eNFA) which are smaller than all the other eNFAs obtained by similar constructions. Their size is at most 3/2|α| + 5/2, where a is the regular expression. The second constructs NFAs. It uses e-elimination in the eNFAs we just introduced and builds a quotient of the well-known position automaton. Our NFA is always smaller and faster to compute than the position automaton. It uses optimally the information from the positions of a regular expression.
01 May 2002
TL;DR: It is proved, that any edge of any non-deterministic automaton defining the given regular language can be obtained by such techniques.
Abstract: In this paper we consider non-deterministic finite Rabin-Scott's automata. We define special abstract objects, being pairs of values of states-marking functions. On the basis of these objects as the states of automaton, we define its edges; the obtained structure is considered also as a nondeterministic automaton. We prove, that any edge of any nondeterministic automaton defining the given regular language can be obtained by such techniques. Such structure can be used for solving various problems in the frames of finite automata theory.
08 Jul 2002
TL;DR: The following problem: "does a given automaton accept any finite graph?" is proven EXPTIME complete and the decidability of the finite model problem for the modal µ-calculus with backward modalities is shown.
Abstract: A graph extension oft wo-way alternating automata on trees is considered. The following problem: "does a given automaton accept any finite graph?" is proven EXPTIME complete. Using this result, the decidability ofthe finite model problem for the modal µ-calculus with backward modalities is shown.