P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for ltrl. In Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS'98). LNCS 1450, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which arise as a consequence of the fact that the satisfiability problem for LTL has a non elementary lower bound [Wal98] However, experience [HJJ 95] has shown that decision procedures can still be useful in practice despite discouraging lower bounds. Gastin, Meyer, and Petit [GMP98a, GMP98b] do give a direct decision procedure for LTL based on automata. However, the construction of the automaton corresponding to a given LTL specification # proceeds by induction on #, thus in a bottom up manner. Hence, it is not an extension of the classical automata theoretic approach, and, more ....

....However, as we will point out in detail, an exponential blow up only occurs for a nesting of until operators. Since nested until operators are di#cult to understand, they are rarely used in practice. A decision procedure for LTL was given by Gastin, Meyer, and Petit in [GMP98a] see also [GMP98b] which is based on automata. Their construction was inspired by the seminal work of Buchi [Buc62] who provided an automaton construction for monadic second order logic interpreted over words. This construction proceeds bottom up, subject to the inductive structure of the formula. For atomic ....

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P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. Technical report, LSV, ENS de Cachan, 1998. extended version of MFCS'98.

....complications which arise as a consequence of the fact that the satisfiability problem for LTL has a non elementary lower bound [Wal98] However, experience [HJJ 95] has shown that decision procedures can still be useful in practice despite discouraging lower bounds. Gastin, Meyer, and Petit [GMP98a, GMP98b] do give a direct decision procedure for LTL based on automata. However, the construction of the automaton corresponding to a given LTL specification # proceeds by induction on #, thus in a bottom up manner. Hence, it is not an extension of the classical automata theoretic approach, and, ....

....in verification tools. However, as we will point out in detail, an exponential blow up only occurs for a nesting of until operators. Since nested until operators are di#cult to understand, they are rarely used in practice. A decision procedure for LTL was given by Gastin, Meyer, and Petit in [GMP98a] see also [GMP98b] which is based on automata. Their construction was inspired by the seminal work of Buchi [Buc62] who provided an automaton construction for monadic second order logic interpreted over words. This construction proceeds bottom up, subject to the inductive structure of the ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. In MFCS: Symposium on Mathematical Foundations of Computer Science, volume 1450 of Lecture Notes in Computer Science, 1998.

....is the complications which arise as a consequence of the fact that the satis ability problem for LTL has a nonelementary lower bound [Wal98] However, experience [HJJK95] has shown that decision procedures can still be useful in practice despite discouraging lower bounds. Gastin, Meyer, and Petit [GMP98a,GMP98b] do give a direct decision procedure for LTL based on automata. However, the construction of the automaton corresponding to a given LTL speci cation proceeds by induction on , thus in a bottom up manner. Hence it is not an extension of the classical automatatheoretic approach, and more ....

....[Wal98] that this closure must be of nonelementary size and, moreover, that this is unavoidable for any decision procedure directly generalising the classical automata theoretic approach. Our approach clearly yields an optimal (non elementary) decision procedure and shares this similarity with [GMP98b]. We are sure that an actual implementation of our approach would compare favourably due to the fact that the 21 automata need not necessarily be constructed in full and especially because it avoids an exponential blow up for negation. We showed that trace consistent linear automata correspond ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. Technical report, LSV, ENS de Cachan, 1998. extended version of MFCS'98.

....is the complications which arise as a consequence of the fact that the satis ability problem for LTL has a nonelementary lower bound [Wal98] However, experience [HJJK95] has shown that decision procedures can still be useful in practice despite discouraging lower bounds. Gastin, Meyer, and Petit [GMP98a,GMP98b] do give a direct decision procedure for LTL based on automata. However, the construction of the automaton corresponding to a given LTL speci cation proceeds by induction on , thus in a bottom up manner. Hence it is not an extension of the classical automatatheoretic approach, and more ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. In MFCS: Symposium on Mathematical Foundations of Computer Science, volume 1450 of Lecture Notes in Computer Science, 1998.

....cations only have a small number of nested until formulas. Hence, a decision procedure for LTL should work in practice very well even if its worst case complexity is high. Similar experiences were made with second order logic over words [HJJK95] A decision procedure for LTrL was presented in [GMP98], which can easily be adapted for LTL. The construction of a B uchi automaton is carried out according to the inductive de nition of a formula. For example, for a formula and its corresponding B uchi automaton A , the one for : is obtained by complementing A . This implies a non elementary ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. Technical report, LSV, ENS de Cachan, 1998. extended version of MFCS'98.

No context found.

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for ltrl. In Proceedings of MFCS'98, number 1450 in Lecture Notes in Computer Science, pages 356-365. Springer, 1998.

....in the past of x 1 ; x k . Hence, we can state: Proposition 1. If a trace language is expressible in LTL f ( then it is expressible in FO( As in the case of LTrL, this translation yields a non elementary decision procedure for the uniform satis ability problem of LTL f . See also [7] for a modular decision procedure based on automata constructions. For the lower bound, we can use [22] since the lower bound is given there for the fragment of LTrL without the previous constant ha 1 i . Putting this together the result of Walukiewicz becomes: Proposition 2 ( 22] The satis ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for ltrl. In L. Brim, F. Gruska, and J. Zlatuska, editors, Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS'98), number 1450 in Lecture Notes in Computer Science, pages 356-365. Springer, 1998.

....past of x 1 ; x k . Hence, we can state: Proposition 1. If a trace language is expressible in LTL f ( Sigma) then it is expressible in FO( As in the case of LTrL, this translation yields a non elementary decision procedure for the uniform satis ability problem of LTL f . See also [7] for a modular decision procedure based on automata constructions. For the lower bound, we can use [24] since the lower bound is given there for the fragment of LTrL without the previous constant ha Gamma1 i . Putting this together the result of Walukiewicz becomes: Proposition 2 ( 24] The ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for ltrl. In L. Brim, F. Gruska, and J. Zlatuska, editors, Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS'98), number 1450 in Lecture Notes in Computer Science, pages 356365. Springer, 1998.

....transitions are called finishing transitions. Proposition 3. The automaton A B ff recognizes exactly the word language Gamma1 (LB (fi U fl) Due to lack of space, we do not provide here a proof of this proposition. The interested reader shall find the complete proof in a technical report[6]. 5 Conclusion We have shown that it is possible to have a direct construction of a Buchi automaton for every formula of LTrL and to make these constructions in a modular way, which allows us to reuse the automata for a formula ff in any construction for a formula fi where ff would be a subformula ....

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for LTrL. Technical report, LSV, ENS de Cachan, June 1998.

No context found.

P. Gastin, R. Meyer, and A. Petit. A (non-elementary) modular decision procedure for ltrl. In Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science (MFCS'98). LNCS 1450, 1998.

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