E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [Harel and Sherman, 1985] see [Harel et al. 2000] In recent years, the development of the automata theoretic approach to logics of programs has prompted renewed inquiry into the complexity of automata on infinite objects, with considerable success. See [Courcoubetis and Yannakakis, 1988; Emerson, 1985; Emerson and Jutla, 1988; Emerson and Sistla, 1984; Manna and Pnueli, 1987; Muller et al. 1988; Pecuchet, 1986; Safra, 1988; Sistla et al. 1987; Streett, 1982; Vardi, 1985a; Vardi, 1985b; Vardi, 1987; Vardi and Stockmeyer, 1985; Vardi and Wolper, 1986b; Vardi and Wolper, 1986a; Arnold, 1997a; ....

E. A. Emerson. Automata, tableax, and temporal logics. In R. Parikh, editor, Proc. Workshop on Logics of Programs, volume 193 of Lect. Notes in Comput. Sci., pages 79--88. Springer-Verlag, 1985.

....y; #)i If c = hai. false If c = hbi, for b 6= a. ut Let n = jQj Delta jRj Delta jV j, let k be the index of S , and let Sigma = V [ f g) Theta Act . By Theorem 1, we can transform A to a nondeterministic one way parity tree automaton A 0 with 2 O(nk) states and index O(nk) By [Rab69,Eme85] if A 0 is nonempty, there exists a Sigma labeled V tree hV ; fi such that for all oe 2 Sigma , the set X oe of nodes x 2 V for which f(x) oe is a regular set. Moreover, the nonemptiness algorithm of A 0 , which runs in time exponential in nk, can be easily extended to construct, ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshopon Logic of Programs, LNCS 193, pp. 79--87, 1985.

....the 2 P labeled trees that do not satisfy . A3. M j= r iff no composition M E satisfies : thus iff the intersection of AM and A: is empty. The reduction of the module checking problem to the emptiness problem for tree automata implies, by the finite model property of tree automata [Eme85] that defining reactive satisfaction with respect to only finite state environments is equivalent to the current definition. In the presence of incomplete information, not all possible pruning of hT M ; VM i correspond to compositions of M with some E . In order to correspond to such a ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

....work for both players at the same time. Whereas in Mostowski games both players have memoryless winning strategies, in Muller games in general there is an asymmetry between the players. For example if a winning condition of a player can be represented in Rabin form then by the results of Emerson [Eme85], Klarlund [Kla92] and McNaughton [McN93] the player has a memoryless winning strategy. The opponent of a player with a Rabin winning condition has a Street winning condition. Lescow [Les95] observed that there are Street winning conditions for which winning strategies require memory of size ....

....disjoint and in our strategy we needed to know on which Y j we are playing. Remark: Note that, in particular, if P(C) n F is closed under union, i.e. F can be expressed by a Rabin condition (see [Zie94] then the strategy G is memoryless. Memoryless determinacy for such games was shown in [Eme85, Kla92]. Remark: Observe that every 1 subtree of a tree from the Example on page 4 (Figure 1) has n leaves (labelled with H i1 ; H in for some i) From Theorem 12 it follows that winning strategies for player 0 in every game with such a winning condition need at most memory of size O(n) By a ....

Emerson, E. A. Automata tableaux, and temporal logic (extended abstract). In R. Parikh, editor, Proceeding of The Conference on Logics of Programs, volume 193 of LNCS, pages 79-88, Berlin, 1985. SpringerVerlag.

.... expressive subset CTL [SC85, VS85] Similarly, while the containment problem for DBW can be solved in NLOGSPACE [WVS83, Kur87] it is PSPACE complete for BW [Wol82] Finally, while the complexity of the nonemptiness problem for BT can be solved in quadratic time [VW86b] it is NP complete for RT [Eme85, VS85, EJ88]. The interested readers can find more examples in [Eme90, Tho90] In the automata theoretic approach to verification, we translate specifications to automata. Which type of automata The answer, obviously, should be the weakest type that is still strong enough to express the required behaviors ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

....W hA;yi2R(a) h ; q; y; #)i If c = hai. false If c = hbi, for b 6= a. ut Let n = jQj jRj jV j, let k be the index of S, and let = V [ f g) Act . By Theorem 2, we can transform A to a nondeterministic one way parity tree automaton A 0 with 2 O(nk) states and index O(nk) By [Rab69,Eme85] if A 0 is nonempty, there exists a labeled V tree hV ; fi such that for all 2 , the set X of nodes x 2 V for which f(x) is a regular set. Moreover, the nonemptiness algorithm of A 0 , which runs in time exponential in nk, can be easily extended to construct, within the ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, LNCS 193, pp. 79--87, 1985.

....finite model property, in fact, it is characterised by finite S4Dbr frames, but once again, note the presence of the extra modalities. Emerson and Srinivasan [ES88] compare the expressiveness of various such branching time logics. Tableau methods for branching time logics can be found in Emerson [Eme85]. Once again, these tableau methods are based on the appropriate analogues of Hintikkastructures (see [EH85] and use the following logical equivalences to expand formulae that match the left hand sides into an outermost EX normal or outermost AX normal form [ES88] E(P Q) j EP EQ A(P Q) j ....

E. Allen Emerson. Automata, tableaux, and temporal logics. In Proc. Logics of Programs 1985, LNCS 193, pages 79--87, 1985.

....formula a finite automaton on infinite structures that accepts exactly all the computations in which the formula is true. For linear temporal logic the structures are infinite words [WVS83, Sis83, LPZ85, Pei85, SVW87, VW94] while for branching temporal logic the structures are infinite trees [ES84, SE84, Eme85, EJ88, VW86b]. This enables the reduction of temporal logic decision problems, both truth and validity checking, to known automata theoretic problems. Initially, the translations in the literature from temporal logic formulas to automata used nondeterministic automata (cf. VW86b, VW94] These translations ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, Berlin, 1985.

....with the state explosion problem. For branching temporal logics, the automata theoretic counterpart are automata on infinite trees. By reducing the satisfiability to the nonemptiness problem for these automata, optimal decision procedures have been obtained for various branching temporal logics [Eme85, EJ88, ES84, SE84, VW86b]. Unfortunately, the automata theoretic approach does not seem to be applicable to branching time model checking. Indeed, model checking can be done in linear running time for CTL [CES86, QS81] and the alternationfree fragment of the calculus [CS93] and is in NP co NP for the general ....

....the 1 letter k ary tree is homogeneous (i.e. all subtrees are the same) we can pretend that successor states which are going down the same branch of the tree, are actually going down separate branches. Thus, we can apply techniques from the theory of nondeterministic Rabin automata, developed in [Eme85, VS85], to show that the 1 letter nonemptiness problem is in NP. Combining Theorems 4 and 5, Proposition 1, and the observation in [EJS93] that checking for satisfaction of a formula and a formula : has the same complexity, we get that the model checking problem for the calculus is in NP co NP. For ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshopon Logic of Programs, pages 79--87. Springer-Verlag, Lecture Notes in Computer Science 193, 1985.

....problem is decidable in doubly exponential time. If the program is fairly realizable, then the nonemptiness algorithm not only says that the automaton TA is nonempty, it also yields a representation of a tree accepted by TA , which is essentially a deterministic sub automaton of TA [Eme85, VS85]. As observed in [PR89a] this sub automaton can be viewed as a finite state program fairly realizing f . Thus, the algorithm for fair realizability also solves the fair synthesis problem. Remark. 1. It may seem as if our upper bound depends on the set B of allowable behaviors to be represented ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshopon Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. SpringerVerlag, 1985.

....logic formula a finite automaton on infinite structures that accepts exactly all the computations that satisfy the formula. For linear temporal logic the structures are infinite words [WVS83, Sis83, LPZ85, Pei85, SVW87, VW94] while for branching temporal logic the structures are infinite trees [ES84, SE84, Eme85, EJ88, VW86b]. This enables the reduction of temporal logic decision problems, such as satisfiability, to known automata theoretic problems, such as nonemptiness, yielding clean and asymptotically optimal algorithms. Initially, the translations in the literature from temporal logic formulas to automata used ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, Berlin, 1985.

....all the 2 P labeled trees that do not satisfy . A3. M j= r iff no composition M E satisfies : thus iff the intersection of AM and A: is empty. The reduction of the module checking problem to the emptiness problem for tree automata implies, by the finite model property of tree automata [Eme85], that defining reactive satisfaction with respect to only finite state environments is equivalent to the current definition. In the presence of incomplete information, not all possible pruning of hT M ; VM i correspond to compositions of M with some E . In order to correspond to such a ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. LP, LNCS 193, pp. 79--87, 1985.

....and unique and vice versa. A Sigma valued tree accepted by a tree automaton can be viewed as a strategy for the Sigma player in the corresponding game automaton. Hence, Player I has a winning strategy in the game automaton iff the corresponding tree automaton has a nonempty language. Emerson [3] showed that every RTA with non empty language accepts a tree that can be embedded in the automaton. It follows that in such an automaton the Sigma player has a strategy that is just a function from Q Sigma , termed a memory less strategy by McNaughton [13] 3 Converting DRA to ....

....by the nonexistence of a winning strategy for the other player is a non trivial and non obvious fact that holds in particular of all two person perfect information games. In a game presented as a Rabin automaton, if player I has a winning strategy, then I also has a memory less winning strategy [3]. If player II has a winning strategy, the question is how complex is the strategy function. Gurevich and Harrington [7] showed that it is sufficient to remember the latest appearance record (LAR) of the states visited and not the entire sequence of states. This bounds the memory required to ....

E. A. Emerson. Automata, tableaux, and temporal logics. In Logics of Programs, LNCS, pages 79--88. Springer-Verlag, 1985.

....strongly connected components in linear time [CLR90] the claim follows. Since there is a quadratic translation of Rabin automata to Buchi automata, Proposition 1 yields a quadratic algorithm for nonemptiness of Rabin automata. For Streett automata, a direct algorithm is needed. Proposition 2. [Eme85] The nonemptiness problem for Streett automata is decidable in polynomial time. Proof: Let A = Sigma; S; S 0 ; ae; G) be the given automaton. Again we start by decomposing GA into maximal strongly connected components reachable from S 0 . We then iterate the following operation For a component ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

....i.e. its time complexity could not be bounded by any fixed stack of exponential functions. Later on, elementary algorithms were described in [HR72, Rab72] The algorithm in [HR72] runs in doubly exponential time and the algorithm in [Rab72] runs in exponential time. Several years later, in [Eme85, VS85], it was shown that the nonemptiness problem for Rabin tree automata is in NP. Finally, in [EJ88] it was shown that the problem is NP complete. There are two relevant size parameters for Rabin tree automata. The first is the transition size, which is size of the transition function (i.e. the ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, Berlin, 1985.

....to a set of states which is necessary to separate the accepting from the non accepting loops. We call such a set a separating set and show in [LV97] how to compute it. Infinite games: Strategy Construction The problem of constructing winning strategies in Rabin chain games is in NP co NP [Eme85] In omega we implemented an algorithm of complexity O(2 n ) where n is the number of states, which is described in detail in [Tho95, BLV96] Infinite games: Conversion of Winning Conditions One of the well known facts about Streett and Muller games is that corresponding winning strategies ....

E. A. Emerson, Automata, tableaux, and temporal logics, Logics of Programs (Berlin, Heidelberg, New York) (R. Parikh, ed.), LNCS, vol. 193, Springer-Verlag, 1985, pp. 79 -- 88.

....problem. For branching temporal logics, the automata theoretic counterpart are automata over infinite trees [Rab69, VW86b] By reducing satisfiability to the nonemptiness problem for these automata, optimal decision procedures have been obtained for various branching temporal logics [Eme85, EJ88, ES84, SE84, VW86b]. Unfortunately, the automata theoretic approach does not seem to be applicable to branching time model checking. Indeed, model checking can be done in linear running time for CTL [CES86, QS81] and for the alternation free fragment of the calculus [Cle93] and is in NP co NP for the general ....

....for alternating Rabin word automata is decidable in nondeterministic polynomial running time. Proof: According to Theorem 3.1, the 1 letter nonemptiness problem for alternating Rabin word automata is of the same complexity as the nonemptiness problem for nondeterministic Rabin tree automata. By [Eme85, VS85], the later is in NP. Combining Theorems 4.8 and 4.9, Proposition 3.2, and the observation in [EJS93] that checking for satisfaction of a formula and a formula : has the same complexity, we get that the model checking problem for the calculus is in NP co NP. 5 The Space Complexity of Model ....

E.A. Emerson. Automata, tableaux, and temporal logics. In Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, Berlin, 1985.

No context found.

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

No context found.

E.A. Emerson. Automata, tableaux, and temporal logics. In WLP, LNCS 193, pp 79--87. Springer-Verlag, 1985.

No context found.

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

No context found.

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79--87. Springer-Verlag, 1985.

No context found.

E.A. Emerson (1985): Automata, Tableaux, and Temporal Logics. Proc. Conf. on Logics of Programs, Brooklyn, LNCS 193, Springer - Verlag, pp.79 - 88.

No context found.

E.A. Emerson. Automata, tableaux, and temporal logics. In Proc. Workshop on Logic of Programs, volume 193 of Lecture Notes in Computer Science, pages 79-87. Springer-Verlag, 1985.

No context found.

E.A. Emerson (1985): Automata, Tableaux, and Temporal Logics. Proc. Conf. on Logics of Programs, Brooklyn, LNCS 193, Springer - Verlag, pp.79 - 88.

No context found.

E. A. Emerson. Automat, tableaux, and temporal logics. In G. Goos and J. Hartmanis, editors, Logics of Programs, volume 803 of LNCS, pages 79 -- 88, Berlin, Heidelberg, New York, 1985. Springer-Verlag.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC