Bouajjani A., Fernandez J.-C., and Halbwachs N., Minimal model generation, In R.P. Kurshan and E.M. Clarke, editors, CAV 90: Computer-aided Verification, Lecture Notes in Computer Science 531, Springer-Verlag (1990), pp. 197--203.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and Kurshan s work [NK00] on computing finite bisimulations simulations of infinite state systems. The main idea there is to start from a finite set of atomic formulae and to successively split the abstract state space induced by these formulae until stabilization. However, in contrast to [BFH90,LY92,HHK95] the splitting in [NK00] is done on atomic formulae instead of equivalence classes which correspond to boolean combinations of these. A similar idea is applied in [SUM96] Abstraction can also be used in combination with other verification techniques, in particular when in the ....

A. Bouajjani, J. Cl. Fernandez, and N. Halbwachs. Minimal model generation. In Workshop on Computer-aided Verification. Rutgers -- American Mathematical Society, Association for Computing Machinery, June 1990.

....is Namjoshi and Kurshan s work [28] on computing nite bisimulations simulations of in nite state systems. The main idea there is to start from a nite set of atomic formulae and to successively split the abstract state space induced by these formulae until stabilization. However, in contrast to [8, 23, 20], the splitting in [28] is done on atomic formulae instead of equivalence classes which correspond to boolean combinations of these. A similar idea is applied in [29] 2 Preliminaries Given a set X of typed variables, a state over X is a type consistent mapping that associates with each variable ....

A. Bouajjani, J. Cl. Fernandez, and N. Halbwachs. Minimal model generation. In Workshop on Computer-aided Veri cation. Rutgers { American Mathematical Society, Association for Computing Machinery, June 1990.

....E (on a set N) with an algorithm whose complexity is O(jEj log jN j) In [KS90] Kannellakis and Smolka notice that the algorithm by Paige and Tarjan [PT87] that solves the relational coarsest partition problem, can be used to determine the maximum bisimulation over a graph G = hN; Ei. In [BFH90] Bouajjani, Fernandez, and Halbwachs propose an algorithm for the relational coarsest partition problem tailored for the context of on the y Model Checking. Precisely, at each iteration the algorithm stabilizes only the reachable blocks with respect to all blocks. In [LY92] Lee and Yannakakis ....

....performances of the algorithm are presented, while there is no through discussion of its complexity in terms of basic symbolic operations. In [FV99] Fisler and Vardi analyze the complexity of the symbolic versions of the algorithms of Paige and Tarjan [PT87] Bouajjani, Fernandez, and Halbwachs [BFH90] and Lee and Yannakakis [LY92] In particular, they determine the number of basic symbolic operations involved in each iteration of the three algorithms and conclude, through experimental results, that an optimized version of the algorithm in [PT87] which splits only reachable blocks, performs ....

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In E. Clarke and R. Kurshan, editors, Proc. of Int. Conference on Computer Aided Veri cation (CAV'90), volume 531 of Lecture Notes in Computer Science, pages 197-203. Springer-Verlag, Berlin, 1990.

....in order to show that finite bisimulations exist for linear control systems and the Boolean algebra of Brunovsky sets. Once existence of a finite bisimulation is established, the following well known bisimulation algorithm terminates while generating the coarsest possible bisimulation partition [7, 12]. Bisimulation Algorithm set: # = i=1 while: #D,D # such that # Pre(D # ) wet: D 1 = D Pre(D # ) D 2 = D Pre(D # ) refine: # = # D ) # D 1 , D 2 end while Once termination of the algorithm is established, computing the coarsest finite bisimulation requires each ....

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In R.P. Kurshan and E.M.Clarke, editors, CAV90: Computer Aided Verification, volume 531 of Lecture Notes in Computer Science, pages 197--203. Springer Verlag, 1990.

....a j such that pT j 1 q pT j q. The symbolic semi algorithm PR 1 closes P under CPre 1 and the boolean operations union, intersection, and set difference. If we close P under CPre f1;2g and all boolean operations, then the result characterizes bisimilarity on the underlying transition structure [5, 13]. The following is shown similar to the analysis of intersection refinement. Theorem 4. The symbolic semi algorithm PR (respectively, PR 1 ) terminates on the region algebra of a game structure G iff the f1; 2g bisimilarity (respectively, 1 bisimilarity) of G has finite index. Corollary 4. The ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In CAV 90, LNCS 531, pp. 197--203. Springer-Verlag, 1990.

.... within a finite number of iterations of the loop, then there is a finite bisimulation quotient, and the algorithm returns a finite partition of the state space which is the coarsest bisimulation (i.e. the bisimulation with the fewest equivalence classes) Algorithm 2 (Bisimulation Algorithm [14], 41] while there exist such that do ; end while; return Therefore, in order to show that CTL model checking can be decided for a transition system , it suffices to show that the bisimulation algorithm terminates on and that each step of the algorithm is computable or effective. This means ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs, "Minimal model generation," in CAV 90: Computer-Aided Verification, R. P. Kurshan and E. M. Clarke, Eds. NewYork: Springer-Verlag, 1990, vol. 531, Lecture Notes in Computer Science, pp. 197--203.

....solutions have been given. In particular, the algorithm proposed by Kanellakis and Smolka [7] is used in many model checkers with explicit state representation, while the algorithm proposed by Bouali and de Simone [3] is used in the case of symbolic representation. The algorithms presented in [2] and [8] are studied to obtain better performances in the case of the so called on the fly Model Checking. The algorithm proposed by Paige and Tarjan in [11] is still the best in terms of worst case time complexity (O( E log N ) In [5] has been proposed an algorithm which works on explicit ....

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In E. Clarke and R. Kurshan, editors, Proc. Int'l Conference on Computer-Aided Verification CAV90, volume 531 of LNCS, pages 197--203. Springer, 1990.

....earlier algorithms for analyzing data insensitive programs and may also be used in other cases, such as symmetric programs, where large reductions can be achieved through bisimulation minimization. It can often be substantially more efficient than the symbolic minimization algorithms of [BFH90,LY92,HHK95] as, unlike these methods, our algorithm does not construct the explicit transition graph of the minimized system, which could be quite large. For programs with bounded non determinacy, our algorithm is able to construct abstractions without the manual application of ....

.... in the worst case, Phi (similarly, Psi ) can be computed by checking the predicate in the scope of the (9X) quantifier for satisfiability for each valuation of the boolean free variables. The decidability of this satisfiability question is also assumed for the symbolic minimization algorithms [BFH90,LY92,HHK95] The massaging step (massage : e; C) 7 (e; newC ; fP) simplifies the expression e and replaces atomic predicates by corresponding boolean variables, defining new boolean variables for predicates not already in C. These new predicates are collected in fP , and C is updated to newC ....

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A. Bouajjani, J-C. Fernandez, and N. Halbwachs. Minimal model generation. In CAV, volume 531 of LNCS,

....is a j such that pT j 1 q pT j q. The symbolic semi algorithm PR 1 closes P under CPre 1 and the boolean operations union, intersection, and set di erence. If we close P under CPre f1;2g and all boolean operations, then the result characterizes bisimilarity on the underlying transition structure [5, 13]. The following is shown similar to the analysis of intersection re nement. Theorem 4. The symbolic semi algorithm PR (respectively, PR 1 ) terminates on the region algebra of a game structure G i the f1; 2g bisimilarity (respectively, 1 bisimilarity) of G has nite index. Corollary 4. The ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In CAV 90, LNCS 531, pp. 197-203. Springer-Verlag, 1990.

.... with under and or overapproximations that focus on abstract models with small BDD representations are presented in [LPJ 96,PH97,CJL 99] We also use ideas of stable partitioning algorithms for computing the quotient space with respect to simulation or bisimulation like equivalences [PT87,BFH90,LY92,HHK95,BG00] However, instead of splitting blocks (sets of concrete states that are identified in the current abstract model) into new subblocks (and thus, creating new abstract states) our approach refines the abstract model by moving subblocks from one abstract state to another abstract ....

....Theorem 1. Partial correctness] If Algorithm 2 terminates with the answer yes then F. If Algorithm 2 terminates with the answer no then F. Because of the similarities with stable partitioning algorithms for calculating the (bi )simulation equivalence classes [PT87,BFH90,LY92,HHK95] it is not surprising that our algorithm terminates provided that the (bi )simulation quotient space of is finite. Theorem 2. Termination] If the concrete model has a finite simulation or bisimulation quotient then Algorithm 2 terminates. Proof. sketch) Neither the model ....

A. Bouajjani, Jean-Claude Fernandez, N. Halbwachs. Minimal model generation. Proc. CAV'90, LNCS 531, pages 197--203, 1990.

....the state transition model (that is, the reachability graph) must first be constructed. Thus, they can be applied only to systems with a finite, relatively small state space. Bouajjani et al. have developed such an algorithm to find the minimal reachability graph for unlabeled transition systems [6]. Their algorithm performs reachability analysis and minimization simultaneously. However, the unlabeled transition system is not expressive enough to describe reactive real time systems. One approach to controlling the state explosion in process composition is compositional analysis [9, 33] In ....

....graph has size exponential in the number of clocks and the size of the constants that appear in the enabling conditions of the transitions [2] In [4] regions having the same reachability are clustered and the resultant graph is called a minimal region graph. They have applied the algorithm [6] to timed automata. However, even the minimal region graph tends to be large and complex. 2.3 Logics for Real Time Properties Real time temporal logic (RTTL) of Ostroff [26] is a real time extension of temporal logic. In RTTL, a distinguishable variable T is used to refer to the current time and ....

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A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal Model Generation. In Proceedings of Workshop on Computer-Aided Verification, 1990.

....size of the constants that appear in the enabling conditions of the transitions. Because the region graph is too fine grained, minimization approaches [3, 17] have been proposed in order to equate more valuations. The minimal region graph is constructed using the partitioning algorithm given in [5]. The minimal region graphs, however, still have the same worst case complexity as region graphs. Another approach is based on forward and backward analysis [9, 4] The forward (and backward) analysis is to repeatly compute the region that includes reachable states by initially starting from the ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal Model Generation. In Proceedings of Workshop on Computer-Aided Verification, 1990.

....a k such that S 0ik 1 poe i q S 0ik poe i q; that is, no new state is encountered. Termination can be detected using the operations Diff and Empty [23] Upon termination, a state q can reach the atomic region pffq iff q 2 poe i q for some 1 i k. The second example is partition refinement [7, 27], denoted APR . The symbolic semi algorithm APR starts from the finite set S 0 = Sigma A of atomic region representatives and computes inductively the finite sets S i 1 = S i [ fPre(oe) And(oe; Diff (oe; j oe; 2 S i g of region representatives. The semi algorithm terminates if there is a ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In CAV 90: Computer-aided Verification, LNCS 663, pages 197--203. Springer-Verlag, 1990.

.... within a finite number of iterations of the loop, then there is a finite bisimulation quotient, and the algorithm returns a finite partition of the state space which is the coarsest bisimulation (i.e. the bisimulation with the fewest equivalence classes) Algorithm 2 (Bisimulation Algorithm [14, 41]) initially Q= B : f[ j 2 Pig; while there exist P; P 0 2 Q= B such that ; P P re(P 0 ) P do P 1 : P P re(P 0 ) P 2 = P n P re(P 0 ) Q= B : Q= B n fPg) fP 1 ; P 2 g end while; return Q= B Therefore, in order to show that CTL model checking can be decided for a ....

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In R.P. Kurshan and E.M. Clarke, editors, CAV 90: Computer-aided Verification, Lecture Notes in Computer Science 531, pages 197--203. SpringerVerlag, 1990.

....To apply these algorithm to a real system, the reachable state space must first be constructed. Thus, they can be applied only to systems with a finite, relatively small state space. Bouajjani et al. have developed a procedure to find the minimal reachability graph for transition systems [BFH90, BFHR92] Their procedure performs reachability analysis and minimization simultaneously, and thus can be applied to infinite state transition system if they have finitely many equivalent classes. We now overview researches on reachability analysis for real time systems. In real time systems, a ....

....To represent the state space of a CSM process finitely, we cluster states that are bisimilar into an equivalence class. We call this process minimization in the sense that all bisimilar states are represented as an equivalence class. We first present a minimization procedure that Bouajjani et al. BFH90] have developed for minimizing a transition systems. We then show how to apply the procedure to CSM directly without generating the corresponding labeled transition system. Not having to generate the entire state space first is important especially for large or infinite state spaces. 7.1 The ....

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A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal Model Generation. In Proceedings of Workshop on Computer-Aided Verification, 1990.

....nature of expert systems, the combinatorial explosion of states may threaten the implementability of such an approach. To tackle the complexity problem, we make use of several different approaches, the most important of them being: 1) the minimal model generation method by Bouajjani et al. [BFH91], 2) the stubborn attack on state explosion using the notion of concurrency by Valmari [Val91] and (3) the equational program decomposition method and concurrent rule execution algorithm by Cheng [Che93] The optimization method introduced in the thesis is two phase and consists first of ....

....analysis and synthesis tools for real time rule based expert systems, so that they can be used in the hard real time environments. Though this thesis main interest are real time rule based systems, the method introduced here originates from the research done in the field of model checking [BFH91] and automatic verification of concurrent systems [Val91] Specifically, we have used some algorithms for the synthesis and reduction of the transition systems introduced by the researchers in those areas. Some methods introduced in this thesis use combinatorial optimization algorithms. We have ....

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A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In E. M. Clarke and R. P. Kurshan, editors, Proc. of 2nd International Conference, CAV '90, pages 197--203, New Brunswick, NJ, June 1991. Springer-Verlag.

....using a richer language (e.g. CCS [Mil80] that supports operators such as parallel composition and hiding. Compositional techniques rely on the definition of a process equivalence (e.g. weak bisimulation) and algorithms to reduce a process with respect to this equivalence [KS90, PT87, CPS93, BFH90, BRdSV87] Starting with a complex expression, subexpressions can then be replaced by equivalent smaller ones in a bottom up fashion. The order in which processes are composed reflects the connectivity, and a judicious use of hiding allows greater reductions by making more transitions internal. ....

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In Computer-Aided Verification, 2nd International Conference, CAV'90, LNCS 531, pages 197--203. Springer-Verlag, 1990.

....if purposes characterize some abstract properties that the system should have and one wants to test, given trees of labels, decorated with verdicts ok and fail . ffl mmg [FKM93] is a minimization tool based on a partition refinement algorithm combined with a reachable state space computation [BFH90] This tools works on the symbolic smi interface. ffl Objectgeode is a tool set developed by Verilog supporting sdl, msc and omt. It includes graphical editors and compilers for each of these formalisms. It also provides a C code generator and a simulator to help the user to interactively debug ....

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal Model Generation. In Proceedings of CAV'90, Rutgers, New Jersey, DIMACS, June 1990.

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Bouajjani A., Fernandez J.-C., and Halbwachs N., Minimal model generation, In R.P. Kurshan and E.M. Clarke, editors, CAV 90: Computer-aided Verification, Lecture Notes in Computer Science 531, Springer-Verlag (1990), pp. 197--203.

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A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In Proceedings of CAV: Computer-Aided Verification, Lecture Notes in Computer Science 531, pp. 197--203. Springer-Verlag, 1990.

No context found.

A. Bouajjani, J.-C. Fernandez, and N. Halbwachs. Minimal model generation. In R.P. Kurshan and E.M. Clarke, editors, CAV 90: Computer-aided Verification, Lecture Notes in Computer Science 531, pages 197--203. SpringerVerlag, 1990.

No context found.

A. Bouajjani, J.C. Fernandez, and N. Halbwachs. Minimal model generation. In R.P. Kurshan and E.M.Clarke, editors, CAV90: Computer Aided Verification, volume 531 of Lecture Notes in Computer Science, pages 197--203. Springer Verlag, 1990.

No context found.

Bouajjani A., Fernandez J.-C., and Halbwachs N., Minimal model generation, In R.P. Kurshan and E.M. Clarke, editors, CAV 90: Computer-aided Verification, Lecture Notes in Computer Science 531, Springer-Verlag (1990), pp. 197-- 203.

No context found.

A. Bouajjani, J. C. Fernandez, and N. Halbwachs. Minimal model generation. In E. Clarke and R. Kurshan, editors, Proc. Int'l Conference on Computer-Aided Verification CAV'90, volume 531 of LNCS, pages 197--203. Springer, 1990.

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Bouajjani, A., J. C. Fernandez and N. Halbwachs, Minimal model generation, in: E. M. Clarke and R. Kurshan, editors, Proc. Int'l Conference on ComputerAided Veri cation CAV90, LNCS 531 (1990), pp. 197-203.

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