E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that can be unwound in an actual model of the formula. A refinement of the quotient construction that exploits the above property is the tableau construction. In subsection 3.3.1, we will describe this technique for C L. Tableau based decision procedures for various logics are given in [BAHP83, EC82, EH85, HS84, LN, LN98, Pra79, Wo183, Wo185]. In subsection 3.3.2 we give the complexity results on C L, L L and some meaningful fragments of L L. A decision procedure for the satisfiability of formulae in C L involves an elaborate reduction to the emptiness problem for finite state automata on infinite trees. This will be discussed in ....

E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985.

....path is NP complete [EL87] TCTL [Koy90] or Timed CTL , allows adding timing subscripts to the usual modalities. In Timed KSs (i.e. Kripke structures where edges carry a discrete duration weight) the existence of a path of a given accumulated duration is NP complete [LMS02a] CTL [EH85] allows arbitrary Boolean combinations (not nesting) of the U and X modalities under a path quantifier. Thus CTL is the branching time extension of L (U, X) the fragment of linear time logic with modal depth one, for which the existence of a path is NP complete [DS02] B # (F) and B # ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1--24, 1985.

....we would write which says, For all traces out of the current state, satisfies 3 ; that is, occurs somewhere along the trace . The logic with the linear temporal operators augmented with the trace quantifiers A and E is known as CTL; see [Emerson, 1990; Emerson and Halpern, 1986; Emerson and Halpern, 1985; Emerson and Lei, 1987; Emerson and Sistla, 1984] Complexity and Deductive Completeness A useful axiomatization of linear time TL without the until operator is given by the axioms 2( 2 2 ) 2( 2 2 3 3 ( 2 8x (x) ....

.... ) 2 8x (x) t) t is free for x in ) 8x 2 28x and rules 2 : Compare the axioms of PDL (Axioms 17) The propositional fragment of this deductive system is complete for linear time propositional TL, as shown in [Gabbay et al. 1980] Sistla and Clarke, 1982] and [Emerson and Halpern, 1985] have shown that the validity problem for most versions of propositional TL is PSPACE complete for linear structures and EXPTIME complete for branching structures. Embedding TL in DL TL is subsumed by DL. To embed propositional TL into PDL, take an atomic program a to mean one step of program ....

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comput. Syst. Sci., 30(1):1--24, 1985.

....think of the future as being a branching structure, then the meaning of must be clarified so that we know whether j means that j must be true on some path in the future, or on all paths in the future. Thus there is a great variety of such logics, including dense logics [BKP86] branching logics [EH82] and past time logics [LPZ85] many of which can be placed in a single framework [Fis89] In this report we will only consider a model of time that is linear and discrete, and allows statements about the present and future. The model structure for such a logic can be given as M = hS, N , pi ....

E. A. Emerson and J. Y. Halpern. Decision Procedures and Expressiveness in the Temporal Logic of Branching Time. In Proceedings of the Fourteenth ACM Symposium on the Theory of Computing, pages 169--180, 1982.

....[ES89, Eme90] Below we consider: an extension of CTL, introduced in [EH86] and where Boolean combinations (not nesting) of temporal modalities are allowed under the scope of a path quanti er. e.g. CTL allows formulae like A(aUb cUd) There exists a translation from CTL to CTL [EH85] hence the two logics have the same expressive power) but such a translation must produce exponential size formulae [Wil99b, AI01] is B(U, X, in the notation of [EH86] but we prefer to see it as B(L (U, X) ECTL: an extension of CTL, introduced in [EH86] where the E F and A ....

....the classical temporal modality, instead of Until and Next. The name BT # is from [CES86] 4.2.2 Model checking fragments of CTL # As far as model checking is concerned, ECTL behaves like CTL: The situation is more interesting for the satis ability problem. It is EXPTIME complete for CTL [EH85] and this leaves much room for fragments that could be less intractable, see [ESS92] for example. The choice of what are the CTL modalities is mostly a historical accident (see Remark 2.4) and it is possible to de ne more expressive logics for which essentially the same model checking ....

E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):124, 1985.

....if we can only reason about one agent or processor in the language, PSPACE complete with two or more agents, and EXPTIME complete if we add common knowledge to the language. If we consider time alone, the validity problem for the language with branching time modalities is EXPTIME complete [EH1], while for the The first two sections of this paper are essentially identical to the first two sections of [HV1] we include them here for completeness. While in [HV1] we described in detail lower bound results, here we describe in deraft some upper bound and completeness results. We plan to ....

E.A. Emerson and J.Y. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, J. Computer and Systems Science, 30:1, 1985, pp. 1-24.

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E.A. Emerson and J.Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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E. A. Emerson and J. Y. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences, vol. 30 (1985), pp. 1--24.

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E.A. Emerson and J.Y. Halpern, Decision Procedures and Expressiveness in the Temporal Logic of Branching Time, Proc. of 14th Annual ACM Symp. on Theory of Computing, San Francisco, pp. 169-180, 1982.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. In Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 169--180, San Francisco, California, 5--7 May 1982.

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E. Emerson and J. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comp and Sys. Sci, 30(1):1-24, 1985.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1{ 24, 1985.

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E. Allen Emerson and Joseph Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. J. Comput. System Sci., 30(1):1--24, 1985.

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E. Allen Emerson and Joseph Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. In ACM, editor, Proc. of the Fourteenth Annual ACM Symposium on Theory of Computing, pages 169--181, San Francisco, California, 1982.

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Emerson, E., and Halpern, J. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of Comput. System Sci., 30, 1-24.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1):1-24, 1985.

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Emerson, E. and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, in: Proceedings of the 14th ACM Symposium on Computing, 1982, pp. 169-180.

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Emerson, E.A. and Halpern J.Y. Decision Procedures and Expressiveness in the Temporal Logic of Branching Time. Proceedings of the Fourteenth Annual ACM Symposium on Theory of Computing, 1982, pp. 169-180.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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A. Emerson and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, Journal of Computer and System Sciences, 30 (1985), pp. 1-24.

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Emerson, E. and J. Halpern, Decision procedures and expressiveness in the temporal logic of branching time, in: Proceedings of the 14th ACM Symposium on Computing, 1982, pp. 169-180.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985. 87

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1--24, 1985.

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E. A. Emerson and J. Y. Halpern. Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30:1-24, 1985.

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