M.Y. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th IEEE Sym.. on Logic in Computer Science, pages 394--405, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....traces of a nondeterministic or concurrent program. Depending on the application and the semantics, different syntactic constructs can be chosen. The relative advantages of linear and branching time semantics are discussed in [Lamport, 1980; Emerson and Halpern, 1986; Emerson and Lei, 1987; Vardi, 1998a] Modal constructs used in TL include 2 holds in all future states 3 holds in some future state holds in the next state until there exists some strictly future point t at which will be satisfied and all points strictly between the current state and t satisfy for ....

M. Vardi. Linear vs. branching time: a complexity-theoretic perspective. In Proc. 13th Symp. Logic in Comput. Sci., pages 394--405. IEEE, 1998.

....do not perform better than the naive non symbolic approach (an approach that can be de ned as build the structure enumeratively and then use the best model checking algorithm at hand . Even in terms of computational complexity, LTL behaves better than CTL on many veri cation problems (see [Var98, Var01] and it seems that model checking is the only place where CTL can hold its ground. The most famous example is of course the OBDD s (Ordered Binary Decision Diagrams) that made symbolic model checking so popular [BCM 92] There had been earlier attempts at symbolic model checking but ....

M. Y. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th IEEE Symp. Logic in Computer Science (LICS'98), pages 394405. IEEE Comp. Soc. Press, 1998.

....thereof, used as speci cation formalisms in the veri cation tools CMC [53] and Uppaal. A complexity theoretic analysis of the model checking problem yields useful guidelines for selecting a speci cation logic which o ers a good compromise between expressiveness and complexity see, e.g. [72] and the references therein for a comprehensive complexity theoretic perspective on model checking for linear and branching time logics for reactive systems, which has been one of the main sources of inspiration for this work. In the remainder of this section, we introduce the di erent ways of ....

....above comparison of the complexity of model checking for untimed formalisms and their timed counterparts is presented in Table 2. Related Work. There is an extensive literature on the complexity of model checking for linear and branching time logics for (concurrent) reactive systems (see, e.g. [51,32,55,64,67,72,73] and the references therein) In particular, 51] o ers an automata theoretic approach to the model checking problem for the branching time logics CTL, CTL and the calculus, and gives improved space complexity bounds for this problem. It will be clear to the readers of this study that we have ....

M. Y. Vardi, Linear vs. branching time: A complexity-theoretic perspective, in Proceedings of the 13th Annual Symposium on Logic in Computer Science, LICS'98, V. Pratt, ed., IEEE Computer Society Press, 1998.

....of designs. Several model checking tools have been developed: On the one hand, SMV and VIS [18, 1] using CTL as a specification logic; and on the other hand, SPIN, COSPAN [14, 9] using LTL; the pros and cons of each formalism with respect to model checking have been the subject of a lively debate [6, 23, 11, 22]. While LTL formulas describe a property of a computation sequence, in CTL every temporal operator has to be preceded by a path quantifier, and hence such a formula expresses a property of a computation tree. The two logics are relateable by considering them to be properties of systems: a system ....

M. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th Symposium Logic in Computer Science, 1998.

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M.Y. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th IEEE Sym.. on Logic in Computer Science, pages 394--405, 1998.

....the branching temporal logic 8CTL is a fragment of CTL in which only universal path quantification is allowed. Note that LTL has implicit universal path quantifiers in front of its formulas. The discussion of the relative merits of linear versus branching temporal logics goes back to 1980 [80,65,31,8,82,35,33,18,100,101]. As analyzed in [82] linear and branching time logics correspond to two distinct views of time. It is not surprising therefore that LTL and CTL are expressively incomparable [65,33,18] The LTL formula FGp is not expressible in CTL, while the CTL formula AFAGp is not expressible in LTL. On the ....

....problem for CTL is 2EXPTIME complete. Thus, module checking for LTL is easier than for CTL (assuming that EXPTIME is different than PSPACE) which is, in turn, easier than for CTL . In particular, this results shows that branching is not free , as has been claimed in [35] 3 See [100] for further discussion on the complexity theoretic comparison between linear time and branching time. Even in the context of closed systems, the alleged superiority of CTL from the complexity perspective is questionable. The traditional comparison is in terms of worst case complexity. Since, ....

M.Y. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th IEEE Sym.. on Logic in Computer Science, pages 394--405, 1998.

....for branching time than for linear time. As we argued in the previous section, this belief is based on worst case complexity rather than practical complexity. It turns out that even from the perspective of worst case complexity the computational superiority of branching time is also not that clear [51]. For example, comparing the complexities of CTL and LTL model checking for concurrent programs, both are PSPACE complete [52,2] As shown in [49,27] the advantage that CTL enjoys over LTL disappears also when the complexity of modular verification is considered. The distinction between closed an ....

M.Y. Vardi. Linear vs. branching time: A complexity-theoretic perspective. In Proc. 13th IEEE Sym.. on Logic in Computer Science, 1998.

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Vardi. Linear vs. branching time: A complexity-theoretic perspective. In LICS: IEEE Symposium on Logic in Computer Science, 1998.

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