Results 1  10
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189
Reasoning about Infinite Computations
 Information and Computation
, 1994
"... We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all ..."
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Cited by 250 (55 self)
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We investigate extensions of temporal logic by connectives defined by finite automata on infinite words. We consider three different logics, corresponding to three different types of acceptance conditions (finite, looping and repeating) for the automata. It turns out, however, that these logics all have the same expressive power and that their decision problems are all PSPACEcomplete. We also investigate connectives defined by alternating automata and show that they do not increase the expressive power of the logic or the complexity of the decision problem. 1 Introduction For many years, logics of programs have been tools for reasoning about the input/output behavior of programs. When dealing with concurrent or nonterminating processes (like operating systems) there is, however, a need to reason about infinite computations. Thus, instead of considering the first and last states of finite computations, we need to consider the infinite sequences of states that the program goes through...
An automatatheoretic approach to linear temporal logic
 Logics for Concurrency: Structure versus Automata, volume 1043 of Lecture Notes in Computer Science
, 1996
"... Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over s ..."
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Cited by 217 (23 self)
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Abstract. The automatatheoretic approach to linear temporal logic uses the theory of automata as a unifying paradigm for program specification, verification, and synthesis. Both programs and specifications are in essence descriptions of computations. These computations can be viewed as words over some alphabet. Thus,programs and specificationscan be viewed as descriptions of languagesover some alphabet. The automatatheoretic perspective considers the relationships between programs and their specifications as relationships between languages.By translating programs and specifications to automata, questions about programs and their specifications can be reduced to questions about automata. More specifically, questions such as satisfiability of specifications and correctness of programs with respect to their specifications can be reduced to questions such as nonemptiness and containment of automata. Unlike classical automata theory, which focused on automata on finite words, the applications to program specification, verification, and synthesis, use automata on infinite words, since the computations in which we are interested are typically infinite. This paper provides an introduction to the theory of automata on infinite words and demonstrates its applications to program specification, verification, and synthesis. 1
Rewriting of Regular Expressions and Regular Path Queries
, 2002
"... Recent work on semistructured data has revitalized the interest in path queries, i.e., queries that ask for all pairs of objects in the database that are connected by a path conforming to a certain specification, in particular to a regular expression. Also, in semistructured data, as well as in da ..."
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Cited by 86 (27 self)
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Recent work on semistructured data has revitalized the interest in path queries, i.e., queries that ask for all pairs of objects in the database that are connected by a path conforming to a certain specification, in particular to a regular expression. Also, in semistructured data, as well as in data integration, data warehousing, and query optimization, the problem of viewbased query rewriting is receiving much attention: Given a query and a collection of views, generate a new query which uses the views and provides the answer to the original one. In this paper we address the problem of viewbased query rewriting in the context of semistructured data. We present a method for computing the rewriting of a regular expression E in terms of other regular expressions. The method computes the exact rewriting (the one that defines the same regular language as E) if it exists, or the rewriting that defines the maximal language contained in the one defined by E, otherwise. We present a complexity analysis of both the problem and the method, showing that the latter is essentially optimal. Finally, we illustrate how to exploit the method for viewbased rewriting of regular path queries in semistructured data. The complexity results established for the rewriting of regular expressions apply also to the case of regular path queries.
On the Power of Quantum Finite State Automata
 Proceedings of the 38th IEEE Conference on Foundations of Computer Science
, 1997
"... In this paper, we introduce 1way and 2way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1way and 2way finite state automata. We prove the following facts regarding 2qfa's. 1. For any ffl ? 0, there is a 2qf ..."
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Cited by 74 (6 self)
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In this paper, we introduce 1way and 2way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1way and 2way finite state automata. We prove the following facts regarding 2qfa's. 1. For any ffl ? 0, there is a 2qfa M which recognizes the nonregular language L = fa m b m j m 1g with (onesided) error bounded by ffl, and which halts in linear time. Specifically, M accepts any string in L with probability 1 and rejects any string not in L with probability at least 1 \Gamma ffl. 2. For every regular language L, there is a reversible (and hence quantum) 2way finite state automaton which recognizes L and which runs in linear time. In fact, it is possible to define 2qfa's which recognize the noncontextfree language fa m b m c m jm 1g, based on the same technique used for 1. Consequently, the class of languages recognized by linear time, bounded error 2qfa's properly includes the regular l...
Automata and coinduction (an exercise in coalgebra
 LNCS
, 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
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Cited by 62 (16 self)
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The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.
Partial Derivatives of Regular Expressions and Finite Automata Constructions
 Theoretical Computer Science
, 1995
"... . We introduce a notion of a partial derivative of a regular expression. It is a generalization to the nondeterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new ..."
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Cited by 59 (0 self)
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. We introduce a notion of a partial derivative of a regular expression. It is a generalization to the nondeterministic case of the known notion of a derivative invented by Brzozowski. We give a constructive definition of partial derivatives, study their properties, and employ them to develop a new algorithm for turning regular expressions into relatively small NFA and to provide certain improvements to Brzozowski's algorithm constructing DFA. We report on a prototype implementation of our algorithm constructing NFA and present some examples. Introduction In 1964 Janusz Brzozowski introduced word derivatives of regular expressions and suggested an elegant algorithm turning a regular expression r into a deterministic finite automata (DFA); the main point of the algorithm is that the word derivatives of r serve as states of the resulting DFA [5]. In the following years derivatives were recognized as a quite useful and productive tool. Conway [8] uses derivatives to present various comp...
From nondeterministic Büchi and Streett automata to deterministic parity automata
 In 21st Symposium on Logic in Computer Science (LICS’06
, 2006
"... Determinization and complementation are fundamental notions in computer science. When considering finite automata on finite words determinization gives also a solution to complementation. Given a nondeterministic finite automaton there exists an exponential construction that gives a deterministic au ..."
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Cited by 45 (3 self)
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Determinization and complementation are fundamental notions in computer science. When considering finite automata on finite words determinization gives also a solution to complementation. Given a nondeterministic finite automaton there exists an exponential construction that gives a deterministic automaton for the same language. Dualizing the set of accepting states gives an automaton for the complement language. In the theory of automata on infinite words, determinization and complementation are much more involved. Safra provides determinization constructions for Büchi and Streett automata that result in deterministic Rabin automata. For a Büchi automaton with n states, Safra constructs a deterministic Rabin automaton with n O(n) states and n pairs. For a Streett automaton with n states and k pairs, Safra constructs a deterministic Rabin automaton with (nk) O(nk) states and n(k + 1) pairs. Here, we reconsider Safra’s determinization constructions. We show how to construct automata with fewer states and, most importantly, parity acceptance condition. Specifically, starting from a nondeterministic Büchi automaton with n states our construction yields a deterministic parity automaton with n 2n+2 states and index 2n (instead of a Rabin automaton with (12) n n 2n states and n pairs). Starting from a nondeterministic Streett automaton with n states and k pairs our construction yields a deterministic parity automaton with n n(k+2)+2 (k+1) 2n(k+1) states and index 2n(k + 1) (instead of a Rabin automaton with (12) n(k+1) n n(k+2) (k+1) 2n(k+1) states and n(k+1) pairs). The parity condition is much simpler than the Rabin condition. In applications such as solving games and emptiness of tree automata handling the Rabin condition involves an additional multiplier of n 2 n! (or (n(k + 1)) 2 (n(k + 1))! in the case of Streett) which is saved using our construction.
TreeWalking Pebble Automata
 Jewels are forever, contributions to Theoretical Computer Science in honor of Arto Salomaa
, 1999
"... this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use ..."
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Cited by 38 (2 self)
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this paper is to investigate the power of treewalking automata with pebbles. Obviously, the unrestricted use of pebbles leads to a class of tree languages much larger than the regular tree languages, in fact to all tree languages in NSPACE(logn). Thus, we restrict the automaton to the recursive use of pebbles, in the sense that the life times of pebbles, i.e., the times between dropping a pebble and lifting it again, are properly nested. A similar, but stronger, nesting requirement is studied in [13] for 2way automata on strings. We prove in Section 5 that our restriction indeed guarantees that all tree languages recognized by the treewalking pebble automaton are regular, but we conjecture that the automaton is not powerful enough to recognize all regular tree languages. In Section 6 we generalize the notion of pebble to that of a \setpebble", in such a way that the treewalking setpebble automaton recognizes exactly the regular tree languages.
Complexity of Automata on Infinite Objects
, 1989
"... We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (! automata). An !automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. I ..."
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Cited by 38 (0 self)
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We investigate in this thesis problems concerning the complexity of translation among, and decision procedure for, different types of finite automata on infinite words (! automata). An !automaton is the same as usual finite automata over finite strings but it accepts or rejects infinite strings. It may be either deterministic or nondeterministic, and may have different types of acceptance condition. Our main result is a new, simpler, determinization construction that yields a single exponent upper bound for the translation of any Buchi nondeterministic !automaton into a deterministic !auomaton. This construction is optimal. We also look at the complexity of the complementation problem for different types of !automata, and, among other results, obtain an exponential complementation for Streett !automata. These results can be used to improve the complexity of decision procedures for different logics that use automatatheoretic techniques. Acknowledgement First and foremost, I o...
System Identification, Approximation and Complexity
 International Journal of General Systems
, 1977
"... This paper is concerned with establishing broadlybased systemtheoretic foundations and practical techniques for the problem of system identification that are rigorous, intuitively clear and conceptually powerful. A general formulation is first given in which two order relations are postulated on a ..."
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Cited by 34 (23 self)
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This paper is concerned with establishing broadlybased systemtheoretic foundations and practical techniques for the problem of system identification that are rigorous, intuitively clear and conceptually powerful. A general formulation is first given in which two order relations are postulated on a class of models: a constant one of complexity; and a variable one of approximation induced by an observed behaviour. An admissible model is such that any less complex model is a worse approximation. The general problem of identification is that of finding the admissible subspace of models induced by a given behaviour. It is proved under very general assumptions that, if deterministic models are required then nearly all behaviours require models of nearly maximum complexity. A general theory of approximation between models and behaviour is then developed based on subjective probability concepts and semantic information theory The role of structural constraints such as causality, locality, finite memory, etc., are then discussed as rules of the game. These concepts and results are applied to the specific problem or stochastic automaton, or grammar, inference. Computational results are given to demonstrate that the theory is complete and fully operational. Finally the formulation of identification proposed in this paper is analysed in terms of Klir’s epistemological hierarchy and both are discussed in terms of the rich philosophical literature on the acquisition of knowledge. 1