O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. of the 13th IEEE Symposium on Logic in Computer Science, pages 81 - 92, June 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bigger BA s. Notice that it is not always possible to reduce completely the presence of non deterministic decision states, as not every LTL formula j can be converted into a deterministic BA, and even deciding if it can be converted into a deterministic BA is in EXPSPACE and is PSPACE Hard [10]. In order to explore the effectiveness of the above conjecture, we thus present a new approach in which we generate from each LTL formula a Buchi automaton which is as deterministic as possible , in the sense that we try to reduce as much as we are able to the presence of non deterministic ....

.... the state corresponding to X j 1 is not in F 1 ; if so, we may loose the fairness condition F 1 if we apply (13) This fact should not be a surprise: if branching postponement were always applicable, then we could always generate a deterministic BA from a LTL formula, which is not the case [10]. Our idea is thus to apply branching postponement only to those formulae j for which we are guaranteed it does not The benefits of using semantic branching rather then syntactic branching in some automated reasoning domains are described in [8] cause incorrectness, and to apply standard ....

O. Kupferman and M.Y. Vardi. Freedom, Weakness, and Determinism: From Linear-time to Branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

....challenges. In fact, while the construction in [KV99] for the directed case is quadratic, here we end up with quadratically many states but exponentially many transitions. Once we have a weak symmetric alternating automaton for , it is possible to generate from it an equivalent AFMC formula [KV98]. 2 Preliminaries For a set D IN of directions, a D tree is a nonempty set T D , where for every x d 2 T with x 2 D and d 2 D, we have x 2 T . The elements of T are called nodes, and the empty word is the root of T . For every x 2 T , the nodes x d, for d 2 D, are the children of ....

....free calculus. Thus, every formula in 2 2 has an equivalent formula in AFMC. For the alternation free calculus, an automata theoretic characterization in terms of symmetric alternating weak automata is well known (a similar result is proven in [AN92] for directed trees) Theorem 3. [KV98] A set T trees( can be expressed in AFMC iff T can be recognized by a symmetric weak alternating automaton. In [Kai95] Kaivola considered calculus formulas in which the 3 modality is parameterized with directions and translates 2 formulas to NBT. In order to apply Theorem 2, we should ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th LICS, pages 81--92, June 1998.

....properties that can be expressed simultaneously in CTL and LTL. The relationship between linear and branching time temporal logics has been studied by several researchers. Clarke and Draghicescu in [3] gave a characterization of the CTL formulas that can be expressed in LTL. Kupferman and Vardi [13] solved the opposite problem of deciding whether an LTL formula can be specified in the alternationfree calculus. This paper is concerned with the formulas that can be expressed simultaneously in LTL and CTL, where we restrict ourselves to ACTL, the fragment of CTL that uses only universal path ....

O. Kupferman and M. Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. 13th Symposium on Logic in Computer Science, 1998.

....of a system is contained in an SCC of a more abstract system, and because we do not have to consider all SCCs, we can often drastically limit the potential space in which a fair cycle can lie. This allows us to make very efficient use of don t care conditions. The strength of a Buchi automaton [10, 2] is an important factor in symbolic model checking. Specialized model checking algorithms for weak and especially terminal automata outperform the general language emptiness algorithm of Emerson and Lei: EFEG fair can be used for weak systems and EF fair can be used for terminal ones. For strong ....

....Q 0 0 , T T 0 , F = F 0 , and = 0 . This (rather strong) condition induces a partial order on automata, such that A A 0 implies L(A) L(A 0 ) If A A 0 , we say that A 0 is an overapproximation of A. Let C Q be an SCC of A. We define the strength of C as follows (cf. [10, 2]) C is weak if all cycles contained within it are accepting. C is terminal if it is weak, complete, and there is no edge from a node in C to any non terminal SCC. Terminality implies acceptance of all runs reaching C. C is strong if it is not weak. Note that the definition of ....

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O. Kupferman and M. Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

....(the universal fragment of CTL) there is Buchi automaton A: whose size is linear in j j. Furthermore, this automaton has a special structure (it is weak ) which enables the model checker to apply improved algorithms for checking the emptiness of the intersection of M with A: 10] See also [56,57] for a through analysis of the relationship between LTL and CTL model checkers. 2.3 Compositionality Model checking is known to suffer from the so called state explosion problem. In a concurrent setting, the system under consideration is typically the parallel composition of many modules. As a ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symp. on Logic in Computer Science, pages 81--92, June 1998.

.... of determining whether a CTL formula has an equivalent LTL formula (a 2EXPTIME upper bound and an EXPTIME lower bound [KV98b] the complexity of determining whether an LTL formula has an equivalent alternation free calculus formula (an EXPSPACE upper bound and a PSPACE lower bound [KV98a]) and several more problems. Essentially, in all the problems above we check the equivalence between a set of trees that satisfy A , for an LTL formula , and a set of trees that is de ned directly by some branching time formalism. The best known translation of A to a tree automaton involves a ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, pages 81-92, June 1998.

....need, in general, a number of symbolic operations that is quadratic in the size of the property automaton [4, 12] We can hence expect appreciable speedups in emptiness checks using either technique if we can reduce the size of the automaton significantly. The strength of a Buchi automaton [13, 2] relates to the complexity of the procedure required to symbolically model check the corresponding property. For a strong automaton, an emptiness check requires the computation of a calculus formula of alternation depth 2, which takes a number of preimage computations quadratic in the size of ....

O. Kupferman and M. Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

.... The last step can be performed by CTL model checking with fairness constraints [6] In the context of this general strategy, our contribution is twofold: First, we propose a classification of the automata obtained by translation of the properties; our classification refines the one proposed in [20] to three types: general, weak, and terminal automata. We show that applying a specific decision procedure to each class results in an algorithm that is superior to the standard one both in theory and in practice. Different tableau constructions produce automata that may differ according to our ....

....number of fixpoints is reduced to one, on the fly model checking can be easily applied [1] In Section 5 we show that this sometimes produces substantial savings in memory and CPU time, even when comparing to CTL model checking. In general, our experiments confirm and strengthen the observation of [20] about the efficiency of LTL model checking. Our second contribution is the extension of guided symbolic search from reachability analysis [32] to LTL model checking. Guided symbolic search applies constraints to the transition relation of the model to make the computation of fixpoints more ....

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O. Kupferman and M. Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

....establish a lower bound on the number of states of the alternating tree automata recognizing the given class of structures. As mentioned above, automata theoretic arguments have been used in this way in different places, for instance by Etessami, Vardi, and myself in [8] or Kupferman and Vardi in [10]. The difference, however, is that in this paper the automaton model (alternating automata on trees) is rather intricate compared to the automaton models used in [8] and [10] nondeterministic automata on words and nondeterministic automata on trees, respectively) The more elaborate argument that ....

.... have been used in this way in different places, for instance by Etessami, Vardi, and myself in [8] or Kupferman and Vardi in [10] The difference, however, is that in this paper the automaton model (alternating automata on trees) is rather intricate compared to the automaton models used in [8] and [10] (nondeterministic automata on words and nondeterministic automata on trees, respectively) The more elaborate argument that is needed here also answers a question raised in the paper by Kupferman and Vardi. A particular problem the authors consider is constructing for a given nondeterministic ....

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Orna Kupferman and Moshe Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In 13th Annual IEEE Symposium on Logic in Computer Science, pages 81--92, Indianaplis, Indiana, 1998.

....LTL formulas that are equivalent to some CTL formulas do even syntactically belong to LeftCTL # . Using the closure theorems, we will see that any formula of LTL # CTL can be translated to a deterministic B chi automaton. A similar result has been obtained by Kupferman and Vardi, who showed in [7] that each formula of the intersection of LTL with the alternation free calculus (a superset of CTL in some sense) can be translated to a deterministic B chi automaton. In [6] it has been shown how given CTL # model checking problems can be handled by the extraction of a LeftCTL # formula. ....

....As PA is dual to PE , and deterministic B chi automata are the complements of deterministic co B chi automata, this means that we can compute for any PA formula a deterministic B chi automaton only by application of the above closure theorems. Hence, we have the following result (similar to [7]) Theorem 2. The following facts are valid: 1. For all # # PE there is an equivalent nondeterministic generalized co B chi automaton with O( # ) states and an acceptance condition of length O( # ) 2. For all # # PE there is an equivalent nondeterministic # automaton with O( # ) states and an ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In IEEE Symposium on Logic in Computer Science, 1998.

....prefixes. The idea is similar: while the proof in Theorem 3. 2 uses the exponential lower bound for going from nondeterministic to deterministic Buchi automata, the proof for this case is a variant of the doubly exponential lower bound for going from LTL formulas to deterministic Buchi automata [KV98] In order to prove the latter, KV98] define the language L n f0; 1; #; g by L n = ff0; 1; #g Delta # Delta w Delta # Delta f0; 1; #g Delta Delta w : w 2 f0; 1g n g: A word w is in L n iff the suffix of length n that comes after the single in w appears somewhere before ....

....the proof in Theorem 3. 2 uses the exponential lower bound for going from nondeterministic to deterministic Buchi automata, the proof for this case is a variant of the doubly exponential lower bound for going from LTL formulas to deterministic Buchi automata [KV98] In order to prove the latter, KV98] define the language L n f0; 1; #; g by L n = ff0; 1; #g Delta # Delta w Delta # Delta f0; 1; #g Delta Delta w : w 2 f0; 1g n g: A word w is in L n iff the suffix of length n that comes after the single in w appears somewhere before the . By [CKS81] the smallest ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, pages 81--92, June 1998.

.... of determining whether a CTL formula has an equivalent LTL formula (a 2EXPTIME upper bound and an EXPTIME lower bound [KV98b] the complexity of determining whether an LTL formula has an equivalent alternation free calculus formula (an EXPSPACE upper bound and a PSPACE lower bound [KV98a]) and several more problems. Essentially, in all the problems above we check the equivalence between a set of trees that satisfy A , for an LTL formula , and a set of trees that is defined directly by some branching time formalism. The best known translation of A to a tree automaton involves a ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from lineartime to branching-time. In Proc. 13th LICS, pp. 81--92, 1998.

....bad prefixes. The idea is similar: while the proof in Theorem 2 uses the exponential lower bound for going from nondeterministic to deterministic Buchi automata, the proof for this case is a variant of the doubly exponential lower bound for going from LTL formulas to deterministic Buchi automata [KV98] Theorem 3. Given a safety LTL formula, the size of a nondeterministic Buchi automaton for pref ( is doubly exponential in the length of . In order to get the upper bound in Theorem 3, we apply the exponential construction in Theorem 1 to the exponential Buchi automaton A for k k. The ....

....1997. IN97] H. Iwashita and T. Nakata. Forward model checking techniques oriented to buggy designs. In Proc. IEEE ACM ICCAD, pp. 400 404, 1997. KV97] O. Kupferman and M.Y. Vardi. Weak alternating automata are not that weak. In Proc. 5th ISTCS, pp. 147 158. IEEE Computer Society Press, 1997. KV98] O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear time to branching time. In Proc. 13th LICS, pp. 81 92, June 1998. Lam85] L. Lamport. Logical foundation. In Distributed systems methods and tools for specification, LNCS 190, 1985. LP85] O. Lichtenstein and A. ....

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th LICS, pp. 81--92, June 1998.

....atomic propositions using the usual Boolean connectives as well as the temporal connective G ( always ) Supported in part by NSF grants CCR 9628400 and CCR 9700061, and by a grant from the Intel Corporation. URL: http: www.cs.rice.edu vardi. 1 This paper is based on work reported in [30,31]. F ( eventually ) X ( next ) and U ( until ) The branching temporal logic CTL augments LTL by the path quantifiers E ( there exists a computation ) and A ( for all computations ) The branching temporal logic CTL is a fragment of CTL in which every temporal connective is preceded by ....

....such calculus formulas takes time that is quadratic in the size of the model. Since the models are very large, the difference with the linear complexity of AFMC is very significant [21] We consider the problem of translating linear time formalisms to AFMC; we describe a characterization, due to [30], of LTL formulas such that the 8CTL formula A is equivalent to an AFMC formula. We also describe an algorithm, due to [30] of deciding whether a given formula meets this characterization, and the problem of translating a given formula to an equivalent AFMC formula when such a translation ....

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, Indiana, June 1998.

....alternation takes time that is quadratic in the size of the model. Since the models are very large, the difference with the linear complexity of AFMC is very significant [HKSV97] Hence, it is desired to translate specification to AFMC. Not all specifications, however, can be translated to AFMC [KV98a] and known translations to AFMC involve a blow up that makes them impractical. In this paper we describe an alternative translation of specifications to AFMC. Second order logic is a powerful formalism for expressing properties of sequences and trees. We can view all common program logics as ....

....order. Thus, each run of a weak automaton eventually gets trapped in some set in the partition. Acceptance is then determined according to the classification of this set. It is shown in [MSS86] that formulas of WS2S can be translated to weak alternating tree automata. Moreover, it is shown in [KV98a] that weak alternating automata can be linearly translated to AFMC. Given two nondeterministic Buchi tree automata U and U 0 that recognize a language and its complement, we construct a weak alternating tree automaton A equivalent to U . The number of states in A is quadratic in the number of ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th LICS, pages 81-92, 1998.

....set B i is visited only finitely often. In [Rab69] Rabin describes 1 In fact, alternating parity tree automata are exactly as expressive as the calculus [Niw88, EJ91] On the other hand, weak alternating tree automata are exactly as expressive as the alternation free fragment of calculus [KV98]. a translation of formulas of monadic second order logic to Rabin tree automata. Today, Rabin automata are used in order to reason about specifications of the full branching time logic CTL [ES84, VS85] as well as to model programs with fairness conditions. The nonemptiness problem for ....

O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, Indiana, June 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. of the 13th IEEE Symposium on Logic in Computer Science, pages 81 - 92, June 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symp. on Logic in Computer Science, pages 81--92, June 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symp. on Logic in Computer Science, pages 81--92, June 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proceedings of LICS'98, pages 81#92. IEEE Computer Society Press, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branching-time. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'98), 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proceedings of LICS'98, pp. 81--92. IEEE Computer Society Press, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branchingtime. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branching-time. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: from linear-time to branching-time. In Proc. 13th IEEE Symp. on Logic in Computer Science, pages 81-92, June 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branching-time. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branching-time. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From Linear-Time to Branching-Time. In Proc. of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branching-time. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'98), 1998.

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Orna Kupferman and Moshe Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In 13th Annual IEEE Symposium on Logic in Computer Science, pages 81--92, Indianaplis, Indiana, 1998.

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O. Kupferman and M.Y. Vardi. Freedom, Weakness, and Determinism: From Linear-time to Branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

No context found.

O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From Linear-Time to Branching-Time. In Proc. of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M. Y. Vardi. Freedom, Weakness, and Determinism: From linear-time to branchingtime. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 81--92, 1998.

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O. Kupferman and M.Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. of the 13th IEEE Symposium on Logic in Computer Science, pages 81 - 92, June 1998.

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O. Kupferman and M. Y. Vardi. Freedom, weakness, and determinism: From linear-time to branching-time. In Proc. 13th IEEE Symposium on Logic in Computer Science, June 1998.

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