N. Reingold, D.W. Wang, and L.D. Zuck. Games I/O automata play. In Cleaveland [Cle92], pages 325--339.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....In [GSSL93] simulation based proof techniques are extended to the live preorder, and in [SLL93b] the new proof techniques are used to verify nontrivial communication protocols. 3. 6 Comparison with Other Models This section compares our model with the models of [Dil88, LT87, AL93] and the work of [RWZ92]. The model of complete trace structures of [Dil88] is a special case of our model. Specifically, the model of [Dil88] does not include a state structure, so that the safe part of a live automaton in [Dil88] is given by a set of traces. Since there is no notion of a state in a complete trace ....

....is introduced which separates safety and liveness properties and requires receptiveness just like our live I O automata. Finally, it is easy to show, given our definition of receptiveness, that the set of live traces of any live I O automaton is union game realizable according to [RWZ92], and thus describable by means of a standard I O automaton of [LT87] However, in general the I O automaton description would involve a lot of encoding and would be extremely unnatural. That is, even though the I O automata of [LT87] and our live I O automata are formally equivalent, fairness is ....

N. Reingold, D.W. Wang, and L.D. Zuck. Games I/O automata play. In Cleaveland [Cle92], pages 325--339.

....involved systems have finite internal nondeterminism, then the live preorder implies the safe preorder. Thus the live preorder guarantees both safety and liveness properties. 3. 6 Comparison with Other Models This section compares our model with the models of [Dil88, LT87, AL93] and the work of [RWZ92]. The model of complete trace structures of [Dil88] is a special case of our model. Specifically, the model of [Dil88] does not include a state structure, so that the safe part of a live automaton in [Dil88] is given by a set of traces. Since there is no notion of a state in a complete trace ....

....safety and liveness properties and requires receptiveness, or equivalently environment freedom, just like our live I O automata. Finally, it is easy to show, given our definition of environment freedom, that the set of live traces of any live I O automaton is union game realizable according to [RWZ92], and thus describable by means of a standard I O automaton of [LT87] However, in general the I O automaton description would involve a lot of encoding and would be extremely unnatural. 4 Timed Systems The notion of liveness discussed in the previous section is now extended to the timed model. ....

N. Reingold, D.W. Wang, and L.D. Zuck. Games I/O automata play. In Cleaveland

....rest of this section shows how the two preorders differ and provides some sufficient conditions for them to coincide. We only consider I O automata without subcomponents (no partitioning of the locally controlled actions) These automata are called automata with a trivial fairness partition in [13]. In our examples we also assume to have an internal action . Example 2. The transition systems ffl ffl T 1 j ffl ffl T 2 j ffl ffl ffl a Delta Delta Delta Gamma Gamma a = OEOE a fflffl # b fflffl b fflffl are equivalent according to the quiescent preorder if ....

....such that ftraces(Autom(T ) S. ut The proof of Proposition 14 is constructive and essentially transforms a finite state I O automaton into a finite state machine with normal and Buchi acceptance states. The proof of Proposition 15 is based on the results about union game realizable languages of [13] and builds an infinite state automaton starting from a complete trace structure T . An open problem is to find a construction giving a finite state I O automaton from a complete trace structure or at least show whether or not such a finite state automaton exists. Proposition16. Given two finite ....

N. Reingold, D. Wang, and L. Zuck. Games I/O automata play. In W. Cleaveland, editor, Proceedings CONCUR 92, Stony Brook, NY, USA, volume 630 of Lecture Notes in Computer Science, pages 325--339. Springer-Verlag, 1992.

....strong I O feasibility , at the lower level of implementation. Our notion of environment freedom solves the same problem in a more general way. It is easy to show, given our definition of environment freedom, that the set of live traces of any live automaton is union game realizable according to [14], and thus describable by means of a standard I O automaton of [10] However in general the I O automaton description would be extremely unnatural. Acknowledgments: We thank Hans Henrik L vengreen and Frits Vaandrager for their valuable criticism and useful comments. ....

N. Reingold, D. Wang, and L. Zuck. Games I/O automata play. In [4], pages 325--339.

....In [GSSL93] simulation based proof techniques are extended to the live preorder, and in [SLL93b] the new proof techniques are used to verify nontrivial communication protocols. 3. 6 Comparison with Other Models This section compares our model with the models of [Dil88, LT87, AL93] and the work of [RWZ92]. The model of complete trace structures of [Dil88] is a special case of our model. Specifically, the model of [Dil88] does not include a state structure, so that the safe part of a live automaton in [Dil88] is given by a set of traces. Since there is no notion of a state in a complete trace ....

....is introduced which separates safety and liveness properties and requires receptiveness just like our live I O automata. Finally, it is easy to show, given our definition of receptiveness, that the set of live traces of any live I O automaton is union game realizable according to [RWZ92], and thus describable by means of a standard I O automaton of [LT87] However, in general the I O automaton description would involve a lot of encoding and would be extremely unnatural. That is, even though the I O automata of [LT87] and our live I O automata are formally equivalent, fairness is ....

N. Reingold, D.W. Wang, and L.D. Zuck. Games I/O automata play. In Cleaveland [Cle92], pages 325--339.

....Thus, traces(A) are exactly the externally visible actions in A s fair executions, and we define beh(A) ext(A) traces(A) to be the behavior of A. The following theorem establishes that finite executions of an automaton A are partial A consistent. The proof of the theorem appears in [LS89, RWZ92], where a state by state construction of a fair execution starting with a finite execution is described. The proof depends on the Axiom of Choice. Theorem 2.7 Let A be an automaton and let ff be a finite execution of A. Then ff is partial A consistent. We sometimes write A as a shorthand for ....

N. Reingold, D.-W. Wang, and L. D. Zuck. Games i/o automata play. In CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 325--339. Springer-Verlag, August 1992.

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