T. A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In Proc. of the 7th Conference on Concurrency Theory #CONCUR'97#,volume 1243 of LNCS, Warsaw, July 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....quotient with respect to their underlying equivalence. State reduction for Buchi automata is useful for making explicit state model checking run faster ( EH00,SB00,EWS01] We define k simulations, where 1 simulation corresponds to ordinary simulation and its variants for Buchi automata ([HKR97,EWS01]) and k simulations, for k 1, generalize the game definition of 1 simulation by allowing the Duplicator to use k pebbles instead of 1 (to hedge its bets ) in response to the Spoiler s move of a single pebble. As k increases, k simulations are monotonically non decreasing relations. ....

....In prior work by this author together with Wilke and Schuller [EWS01] we provided efficient algorithms for computing a variety of simulations (and bisimulations) on the state space of Buchi automata. These simulations included among them fair simulation, introduced by Henzinger, et al. [HKR97]) but we also introduced a new notion of simulation called delayed simulation, and showed that while fair simulation quotients do not preserve the language of an automaton, delayed simulation quotients do and yet they can be arbitrarily coarser (i.e. larger) than standard direct simulation, used ....

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. of 9th Int. Conf. on Concurrency Theory (CONCUR'97), number 1243 in LNCS, pages 273--287, 1997.

....on a recent algorithm by Jurdzinski, to efficiently compute all the above simulation relations. In particular, we obtain an O(mn 3 ) time and O(mn) space algorithm for computing both the delayed and fair simulation relations. The best prior algorithm for fair simulation requires time O(n 6 ) [HKR97]) Our framework also allows one to compute bisimulations efficiently: we compute the fair bisimulation relation in O(mn 3 ) time and O(mn) space, whereas the best prior algorithm for fair bisimulation requires time O(n 10 ) HR00] 1 Introduction There are at least two distinct purposes ....

....preorder. For state machines without acceptance conditions, there is a well understood notion of simulation with a long history (see, e.g. Mil89,HHK95] For automata, where acceptance (fairness) conditions are present, there are a variety of different simulation notions (see, e.g. [HKR97], GL94] At a minimum, for such a simulation to be of use for purpose (1) it must have the following property: whenever state q 0 simulates state q the language of the automaton with start state q 0 contains the language of the automaton with start state q. This property alone ....

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. of 9th Int. Conf. on Concurrency Theory (CONCUR'97), number 1243 in LNCS, pages 273--287, 1997.

.... In this section we describe what, algorithmically, is our most elaborate reduction: a kind of fair simulation reduction, with an algorithm based on color refinement (see, e.g. HU79] It turns out that there are several distinct notions of fair simulation in the literature (see, e.g. [HKR97]) The weaker the notion, the more reduction it potentially enables. The notion we chose to implement is by no means the weakest available notion, but its advantage is that it admits an easy to implement and reasonably efficient algorithm which is a very natural modification of the ordinary ....

....enables. The notion we chose to implement is by no means the weakest available notion, but its advantage is that it admits an easy to implement and reasonably efficient algorithm which is a very natural modification of the ordinary color refinement algorithm. Henzinger, Kupferman, and Rajamani, [HKR97], describe a weaker notion of fair simulation, and give a polynomial time algorithm for computing the relation. But their algorithm, which employs an algorithm of [HHK95] for computing a maximal simulation relation and then resorts to tree automata and their emptiness problem to deal with fair ....

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. of 9th Int. Conf. on Concurrency Theory (CONCUR'97), number 1243 in LNCS, pages 273--287, 1997.

....restricted to ACTL safety formulas. It is straight forward to extend our method to full ACTL. This will require, however, to add fairness constraints to the tableau structure and to use the fair simulation preorder [3] Unfortunately, there is no efficient algorithm to implement fair simulation [4]. Thus, it is currently impractical to use full ACTL. There is a need to find logics that are both reasonable in terms of their expressivity and practical in terms of tableau construction and comparison criteria. Acknowledgment: We thank Ilan Beer for suggesting to look into the problem of ....

T. A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In Proc. of the 7th Conference on Concurrency Theory (CONCUR'97), volume 1243 of LNCS, Warsaw, July 1997.

....this is a crucial aspect of a successful methodology for dealing with liveness. It should be clear that Figure 1 provides a very succinct presentation for the refinement of the liveness property expressed by hhhx 2 wait ; x 62 waitiii, namely that every request eventually receives a response. [7] presents various extensions of simulation that take fairness into account. Fairness is expressed using either Buchi or Streett (i.e. complemented pairs) acceptance conditions. However, the fair simulation notions are defined using a game theoretic semantics, and require a priori that fair ....

....worthwhile to investigate the other well known acceptance conditions: the Buchi, Muller, and Rabin (pairs) conditions. We also intend to extend backward simulation [8] to refine liveness, and, for (liveness preserving) forward simulation, to extend our trace containment results to tree containment [7]. Acknowledgments. I would like to thank Nancy Lynch for challenging me to work on the problem of refining liveness properties, and Victor Luchangco for very helpful discussions about the eventually serializable data service. ....

Henzinger, T., Kupferman, O., and Rajamani, S. Fair simulation. In CONCUR 97: Concurrency Theory (1997), A. Mazurkiewicz and J. Winkowski, Eds., Lecture Notes in Computer Science 1243, Springer-Verlag, pp. 273--287.

....respect to failed properties. We also plan to explore coarser abstractions for the automata theoretic framework. Bisimulation preserves details about the lengths of paths that are irrelevant for checking whether a fair path exists. Coarser abstractions, such as those based on two sided simulation [15, 24] or stuttering equivalence [18] may be even better suited to algorithmic state space reduction in the automata theoretic framework. Finally, we plan to explore applying our method to abstract part of the state space. For example, it could be used for data path abstraction by collapsing the space ....

T.A. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. 8th Conference on Concurrency Theory, volume 1243 of Lecture Notes in Computer Science, pages 273--287, Warsaw, July 1997. Springer-Verlag.

....this is a crucial aspect of a successful methodology for dealing with liveness. It should be clear that Figure 1 provides a very succinct presentation for the refinement of the liveness property expressed by hhhx 2 wait ; x 62 waitiii, namely that every request eventually receives a response. HKR97] presents various extensions of simulation that take fairness into account. Fairness is expressed using either Buchi or Streett (i.e. complemented pairs) acceptance conditions. However, the fair simulation notions are defined using a game theoretic semantics, and require a priori that 9 L must ....

....be possible to use the other well known acceptance conditions: the Buchi, Muller, and Rabin (pairs) conditions. We also intend to extend backward simulation [LV93] to refine liveness, and, for (liveness preserving) forward simulation, to extend our trace containment results to tree containment [HKR97] ....

T.A. Henzinger, O. Kupferman, and S.K. Rajamani. Fair simulation. In A. Mazurkiewicz and J. Winkowski, editors, CONCUR 97: Concurrency Theory, Lecture Notes in Computer Science 1243, pages 273--287. Springer-Verlag, 1997.

....no efficient technique exists to check or compute fair preorder between models. In [17] Grumberg and Long suggest how to check the fair preorder only for a few trivial cases. Kupferman and Vardi showed that the general case is PSPACE hard to compute [22] Henzinger, Kupferman, and Rajamani [18] have proposed a new type of fair preorder that can be computed in polynomial time. However, it is not clear that this preorder is appropriate for compositional reasoning. 6.1.1 Example: The Futurebus Protocol. David Long has used this type of reasoning to verify safety and liveness properties ....

T. A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In Proc. of the 7th Conference on Concurrency Theory (CONCUR'97), volume 1243 of LNCS, Warsaw, July 1997.

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T.A. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. I&C, 173(1):64-- 81, 2002.

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T.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In CONCUR 97: Theories of Concurrency, Lecture Notes in Computer Science 1243, pages 273--287. Springer-Verlag, July 1997.

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. 8th Conference on Concurrency Theory, volume 1243 of Lecture Notes in Computer Science, pages 273-287, Warsaw, July 1997. Springer-Verlag.

....3. Consider two fair Moore machines P and Q such that the composition P k Q exists. Then T is a fair trace tree of P k Q iff (1) T ] P is a fair trace tree of P, and (2) T ] Q is a fair trace tree of Q. Fair simulation. Suppose that Q is refinable by P . Intuitively, Q fairly simulates P [HKR97] if there is a strategy in the simulation game that matches every fair run of P with a fair run of Q. Formally, a simulation strategy of Q with respect to P is a partial function from Sigma P Theta Sigma Q to S Q . If s = s 0 i 1 s 1 i 2 s 2 i 3 : i n Gamma1 s n 2 ....

....two fair Moore machines P = hP; F P i and Q = hQ; F Q i. If P F s Q, then P s Q. The proof of Proposition 4 depends on the receptivenss of Q. Analogous to the equivalence between simulation and tree containment, fair simulation can be proved to be equivalent to fair tree containment [HKR97]. Proposition 5. Consider two fair Moore machines P and Q. Then P F s Q iff Q fair tree contains P. 10 5 Assume Guarantee Rule for Fair Simulation Let Safe(P) be the fair Moore machine obtained by replacing the fairness constraint of P with the trivial fairness constraint that maps every ....

T.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In CONCUR 97: Theories of Concurrency, Lecture Notes in Computer Science 1243, pages 273--287. Springer-Verlag, July 1997. 11

....] Q is a fair trace tree of Q. Fair tree containment. We say that Q fair tree contains P if (1) Q is refinable by P , and (2) for every fair trace tree T of P the projection [T ] Q is a fair trace tree of Q. Fair simulation. Suppose that Q is refinable by P . Intuitively, Q fairly simulates P [HKR97] if there is a strategy that matches every fair run of P with a fair run of Q. Formally, a strategy oe of Q with respect to P is a partial function from Sigma P Theta Sigma Q to S Q . If s = s 0 i 1 s 1 i 2 s 2 i 3 : i n Gamma1 s n 2 Sigma P , and s 0 = s 0 0 ....

....we have the following proposition. Proposition 4. Consider two fair Moore machines P = hP; F P i and Q = hQ; F Q i. If P F s Q, then P s Q. Analogous to the equivalence between simulation and tree containment, fair simulation can be proved to be equivalent to fair tree containment [HKR97]. Proposition 5. Consider two fair Moore machines P and Q. Then P F s Q iff Q fair tree contains P. 5 Assume Guarantee Rule for Fair Simulation Let Safe(P) be the fair Moore machine obtained by replacing the fairness constraint of P with the trivial fairness constraint that maps every run to ....

T.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In CONCUR 97: Theories of Concurrency, Lecture Notes in Computer Science 1243, pages 273--287. Springer-Verlag, July 1997.

....with respect to LTL, and PSPACE completeness extend to the fair case. It is less obvious how to generalize the branching approach to account for fairness. Several proposals for fair bisimulation can be found in the literature. We consider here three: 9 bisimulation [GL94] game bisimulation [HKR97,HR00] and 8 bisimulation [LT87] In a bisimulation relation between S and S 0 with no fairness, two related states s and s 0 agree on their observable variables, every successor of s is related to some successor of s 0 , and every successor of s 0 is related to some successor of s. In ....

.... the relation is a bisimulation in which related computations agree on their fairness (we review the formal definitions in Section 2) The different definitions induce different relations: 8 bisimulation implies gamebisimulation, which implies 9 bisimulation, but the other direction does not hold [HKR97] The difference in the distinguishing power of the definitions is also reflected in their logical characterization: while 9 bisimulation corresponds to fair CTL (that is, two systems are 9 bisimilar iff they agree on all fair CTL formulas, where path quantifiers range over fair ....

[Article contains additional citation context not shown here]

T.A. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. 8th Conference on Concurrency Theory, LNCS 1243, pp. 273--287, 1997.

....is not hard to extend the trace based approach to account for fairness, it is not so obvious how to do it in the tree based approach. Several proposals for fair bisimulation can be found in the literature. In this paper, we study the earliest definition, of [GL94] The alternative definition of [HKR97] is based on games, and the complexity of checking game simulation is only polynomial. 5 n components S 1 ; S n for some n 1. Each component S i is a tuple hO i ; W i ; W 0 i ; ffi i ; L i ; ff i i, where: ffl O i O is a set of local observable events. The O j are not necessarily ....

T.A. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. 8th Conference on Concurrency Theory, volume 1243 of Lecture Notes in Computer Science, pages 273--287, Warsaw, July 1997. Springer-Verlag.

....3. Consider two fair Moore machines P and Q such that the composition P k Q exists. Then T is a fair trace tree of P k Q iff (1) T ] P is a fair trace tree of P, and (2) T ] Q is a fair trace tree of Q. Fair simulation. Suppose that Q is refinable by P . Intuitively, Q fairly simulates P [HKR97] if there is a strategy in the simulation game that matches every fair run of P with a fair run of Q. Formally, a simulation strategy of Q with respect to P is a partial function from Sigma P Theta Sigma Q to S Q . If s = s 0 i 1 s 1 i 2 s 2 i 3 : i n Gamma1 s n 2 ....

....we have the following proposition. Proposition 4. Consider two fair Moore machines P = hP; F P i and Q = hQ; F Q i. If P F s Q, then P s Q. Analogous to the equivalence between simulation and tree containment, fair simulation can be proved to be equivalent to fair tree containment [HKR97]. Proposition 5. Consider two fair Moore machines P and Q. Then P F s Q iff Q fair tree contains P. 5 Assume Guarantee Rule for Fair Simulation Let Safe(P) be the fair Moore machine obtained by replacing the fairness constraint of P with the trivial fairness constraint that maps every ....

T.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In CONCUR 97: Theories of Concurrency, Lecture Notes in Computer Science 1243, pages 273--287. Springer-Verlag, July 1997.

No context found.

T. A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In Proc. of the 7th Conference on Concurrency Theory #CONCUR'97#,volume 1243 of LNCS, Warsaw, July 1997.

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T.A. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. 8th Conference on Concurrency Theory, LNCS 1234, 1997.

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Th.A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In CONCUR '97, vol. 1243 of LNCS, pp. 273--287, 1997. 37

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Thomas A. Henzinger, Orna Kupferman, and Sriram K. Rajamani. Fair simulation. In Proc. of 8th Int. Conf. on Concurrency Theory (CONCUR '97), vol. 1243 of LNCS, pp. 273--287, 1997.

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proc. of 9th Int. Conf. on Concurrency Theory (CONCUR'97), number 1243 in LNCS, pages 273--287, 1997.

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Thomas A. Henzinger, Orna Kupferman, and Sriram K. Rajamani. Fair simulation. In CONCUR

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Thomas A. Henzinger, Orna Kupferman, and Sriram K. Rajamani. Fair simulation. In Proc. of 8th Int. Conf. on Concurrency Theory (CONCUR '97), vol. 1243 of LNCS, pp. 273--287, 1997.

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T. Henzinger, O. Kupferman, and S. Rajamani. Fair simulation. In Proceedings of the 9th International Conference on Concurrency Theory (CONCUR'97), pages 273--287. Springer-Verlag, 1997. LNCS 1243.

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T. A. Henzinger, O. Kupferman, and S. K. Rajamani. Fair simulation. In Proc. of the 7th Conference on Concurrency Theory #CONCUR'97#,volume 1243 of LNCS, Warsaw, July 1997.

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