It is well known that model checking and satisfiability for PLTL are PSPACE-complete, By contrast, very little is known about whether there exist, some interesting fragments of PLTL with it lower worst-case complexity...
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It is well known that model checking and satisfiability for PLTL are PSPACE-complete, By contrast, very little is known about whether there exist, some interesting fragments of PLTL with it lower worst-case complexity. Such results would help understand why PLTL model checkers are successfully used in practice. In this article we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed. (2) the number of atomic propositions, and (3) the temporal height. (C) 2002 Elsevier science (USA).
In this paper, we study issues on disjunctions of propositional Horn theories. In particular, we consider the problems of deciding whether a disjunction of Horn theories is Horn, and, if not, computing a Horn core (i....
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In this paper, we study issues on disjunctions of propositional Horn theories. In particular, we consider the problems of deciding whether a disjunction of Horn theories is Horn, and, if not, computing a Horn core (i.e., a maximal Horn theory included in this disjunction) and the Horn envelope (i.e., the minimum Horn theory including the disjunction), where a Horn core and the Horn envelope are important approximations of the original theory in artificial intelligence. The problems are investigated for two different representations of Horn theories, namely, for Horn conjunctive normal forms (CNFs) and characteristic models. While the problems are shown to be intractable in general, in the case of bounded disjunctions, we present polynomial time algorithms for testing the Horn property in both representations and for computing a Horn core in the CNF representation. Even in the case of bounded disjunction, no polynomial algorithm exists (unless P=NP) for computing a Horn core in the characteristic model representation. Computing the Horn envelope is polynomial in the characteristic model representation, while it is exponential in the CNF representation, even for bounded disjunction.
Consider the class of all those properties of worlds in finite Kripke structures (or of states in finite transition systems), that are recognizable in polynomial time, and closed under bisimulation equivalence. It is ...
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Consider the class of all those properties of worlds in finite Kripke structures (or of states in finite transition systems), that are recognizable in polynomial time, and closed under bisimulation equivalence. It is shown that the class of these bisimulation-invariant PTIME queries has a natural logical characterization. It is captured by the straightforward extension of propositional mu-calculus to arbitrary finite dimension. Bisimulation-invariant PTIME, or the modal fragment of PTIME, thus proves to be one of the very rare cases in which a logical characterization is known in a setting of unordered structures. It is also shown that higher-dimensional mu-calculus is undecidable for satisfiability in finite structures, and even Sigma(1)(1)-hard over general structures. (C) 1999 Elsevier science B.V. All rights reserved.
We consider Boolean formulas where logical implication (-->) is the only operator and all variables, except at most one (denoted z), occur at most twice. We show that the problem of determining falsifiability for f...
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We consider Boolean formulas where logical implication (-->) is the only operator and all variables, except at most one (denoted z), occur at most twice. We show that the problem of determining falsifiability for formulas of this class is NP-complete but if the number of occurrences of z is restricted to be at most k then there is an O(\F\(k)) algorithm for certifying falsisability. We show this hierarchy of formulas, indexed on k, is interesting because even lower levels (e.g., k = 2) are not subsumed by several well-known polynomial time solvable classes of formulas. (C) 1999 Elsevier science B.V. All rights reserved.
In this paper we study, in the framework of mathematical logic, L(SBTA) i.e. the class of languages accepted by Systolic Binary Tree Automata. We set a correspondence (in the style of Buchi Theorem for regular languag...
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ISBN:
(纸本)3540642307
In this paper we study, in the framework of mathematical logic, L(SBTA) i.e. the class of languages accepted by Systolic Binary Tree Automata. We set a correspondence (in the style of Buchi Theorem for regular languages) between L(SBTA) and MSO[Sig], i.e, a decidable Monadic Second Order logic over a suitable infinite signature Sig. We also introduce a natural subclass of L(SBTA) which still properly contains the class of regular languages and which is proved to be characterized by Monadic Second Order logic over a finite signature Sig' subset of Sig. Finally, in the style of McNaughton Theorem for star free regular languages, we introduce an expression language which precisely denotes the class of languages defined by the first order fragment of MSO[Sig'].
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