M. Y. Vardi and P. L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proc. IEEE Symp. on Logic in Computer Science, pages 332--334, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....checking proceeds in a similar fashion. The parse tree is traversed in post order. Evaluation of truth values for a path formula can be done by using a model checker for LTL, another temporal logic. Model checking of LTL formulas can be done using language containment and tableau construction [VW86] 2.4 Permutation Groups A classic reference for group theory is a textbook by Herstein [Her75] Permutation groups are studied in a book by Wielandt [Wie64] Practical algorithms for manipulating permutation groups are presented by Butler [But91] 2.4.1 Definitions A permutation is a ....

M. Y. Vardi and P. L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proc. IEEE Symp. on Logic in Computer Science, pages 332--334, 1986.

....qualitative. In such paradigms, it is proved that verification can be reduced to performing conventional temporal logic analysis on a model with fairness constraints that eliminate events of measure zero; the actual probabilities of events is immaterial. Examples of such approaches are given in [13, 16, 20, 1]. 16] introduces the notion of ff fairness; this construct embodies the fact that if a given state is visited infinitely often, then with probability one each state which the given state can make a transition to with non zero probability is visited infinitely often. 20] follows an approach in ....

....are given in [13, 16, 20, 1] 16] introduces the notion of ff fairness; this construct embodies the fact that if a given state is visited infinitely often, then with probability one each state which the given state can make a transition to with non zero probability is visited infinitely often. [20] follows an approach in which non deterministic behavior is differentiated from stochastic behavior. Again, verifying such systems reduces to conventional PLTL checking on a Kripke structure with appropriate fairness constraints, which can be done by automata theoretic techniques. 1] verifies ....

M. Y. Vardi and P. L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proc. IEEE Symposium on Logic in Computer Science, pages 332-- 334, 1986. This article was processed using the L a T E X macro package with LLNCS style

....them in two layers : at the local level, we have a system for each agent, and at the global level, a system to put them together. This requires a separate detailed account, so we omit it from this presentation. The decidability proofs follow standard automata theoretic techniques developed by [VW86]. Instead of using Product Buchi automata or Asynchronous Buchi automata as done in [T94, T95] we keep the automata structure simple, but use product construction and partial order methods in the analysis. 5 Recall that a (nondeterministic) Buchi automaton over a finite nonempty alphabet S is ....

Vardi, M.Y. and Wolper, P., "An automata theoretic approach to program verification", Proc LICS, IEEE, 1986, 332-345. 10

....Temporal Logic of Linear Time (PTL) is used to describe the temporal evolution of global states of distributed systems. Reasoning in PTL about safety, liveness and fairness properties of systems is well understood by now. With the development of both automata theoretic model checking techniques [VW86] and theorem proving techniques [MP91] automatic or semiautomatic verification of temporal properties has seen considerable progress. A number of researchers ( GW94] KP92a] V90] have noted that there is a natural equivalence relation on runs of systems which equates runs obtained by ....

....A 1 etc to denote atoms. We define a successor relation Succ AT Theta Sigma Theta AT as follows: A; a; B) 2 Succ iff (8flff 2 CL, flff 2 A iff ff 2 B) and (8p : j(p) a) p 2 A iff p 2 B) In this case, we say that B is an a successor of A. The standard decision procedure for PTL ([VW86]) consists of building a nondeterministic Buchi automaton whose states are atoms and transitions are given by Succ above, with suitable modifications for keeping track of U requirements. It is then shown that ff 0 is satisfiable if and only if the language accepted by the associated automaton is ....

Vardi, M.Y., and Wolper, P., "An automata theoretic approach to program verification", Proc LICS, 1986, 332-345.

....then continues verifying the system with respect to other properties, until the user is convinced that the intersection of the languages of the properties is equal (or maybe very close) to the desired set of behaviors. The above scheme for doing formal verification first appeared in literature in [VW86]. VW86] suggested specifying both the system and the property using Buchi automata, and went on to give an algorithm for language containment in this environment. The usual method to verify that L(S) is contained in L(T ) where L(S) and L(T ) are the languages of the system and property ....

....verifying the system with respect to other properties, until the user is convinced that the intersection of the languages of the properties is equal (or maybe very close) to the desired set of behaviors. The above scheme for doing formal verification first appeared in literature in [VW86] [VW86] suggested specifying both the system and the property using Buchi automata, and went on to give an algorithm for language containment in this environment. The usual method to verify that L(S) is contained in L(T ) where L(S) and L(T ) are the languages of the system and property respectively, is ....

M.Y. Vardi and P.L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proceedings of the IEEE Symposium on Logic in Computer Science, pages 332--334, 1986.

....this operator returns just a path and not necessarily an infinite path. The FFP operator can be computed by using the following algorithm: FFP(T; C; A) return( Q i;c i 2C (GFP (x; T; A Delta U i ) V i ) Q j;E j 2C (GFP (x; T; 9 y E j (y; x) 3 Previous Work Vardi and Wolper [10] observe that the problem of verifying whether a machine (M ) satisfies a given property (P ) reduces to the problem of checking whether the language of the machine automaton is contained in the language of the property automaton. The language containment check in turn reduces to a language ....

M. Y. Vardi and P. L. Wolper, "An Automata-Theoretic Approach to Program Verification," in Proc. IEEE Symposium on Logic in Computer Science, pp. 332--334, 1986.

.... ( Q j;E j 2C (GFP (x; T; E j ) 3 Previous Work in Language Containment The problem of verifying whether a machine (M ) satisfies a given property (P ) reduces to the problem of checking whether the language of the machine automaton is contained in the language of the property automaton [9]. This language containment check in turn reduces to a language emptiness check for the product of the system automaton and the complement of the property automaton. Checking whether L(M ) L(P ) is the same as checking whether the language of D = M P is empty. When P is expressed as an ....

M. Y. Vardi and P. L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proc. IEEE Symposium on Logic in Computer Science, pages 332--334, 1986.

....state. In the language containment paradigm in its most general form, the property is a language L P . The design satisfies the property iff its language (possibly projected down to some subset of the inputs and or outputs) is contained in L P . The property L P could be defined in various ways [117]. When it is the language of an FSM M P with an initial state and a Buchi fairness constraint, testing language containment can be performed in polynomial time provided the language of M P is not projected over any inputs. When the language of M P is projected over inputs, deciding CHAPTER 3. ....

....qualitative. In such paradigms, it is proved that verification can be reduced to performing conventional temporal logic analysis on a model with fairness constraints that eliminate events of measure zero; the actual probabilities of events are immaterial. Examples of such approaches are given in [56, 91, 117, 3]. Penuli and Zuck [91] introduce the notion CHAPTER 8. STOCHASTIC SYSTEMS 93 of ff fairness; this construct embodies the fact that if a given state is visited infinitely often, then with probability one each state which the given state can make a transition to with nonzero probability is visited ....

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M. Y. Vardi and P. L. Wolper. An Automata-Theoretic Approach to Program Verification. In Proc. IEEE Symposium on Logic in Computer Science, pages 332--334, 1986.

....in A or be reached by some state in A. The RRS operator returns the set of states, which are on paths through A. The Reach Reachable States operator or RRS(T (x; y) A) is computed as follows: RRS(T (x; y) A) return (BR(T (x; y) A) FR(T (x; y) A) 5. 3 Language Containment Vardi and Wolper [67] observe that the problem of verifying whether a machine (M) satisfies a given property (P ) reduces to the problem of checking whether the language of the machine automaton is contained in the language of the property automaton. The language containment check in turn reduces to a language ....

M. Y. Vardi and P. L. Wolper, "An Automata-Theoretic Approach to Program Verification, " in Proc. IEEE Symposium on Logic in Computer Science, pp. 332--334, 1986.

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