E. M. Clarke et al., "Symmetry reductions in model checking," in Proc. Int. Conf. Computer-Aided Verification, A. J. Hu and M. Y. Vardi, Eds., 1998, pp. 159--171.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....discuss symmetry reduction for systems when the transition relation is given either explicitly in terms of states or symbolically as a BDD. Their results are summarised in [20] The complexity of the orbit problem and examples of groups where the orbit problem is easy to solve are considered in [13]. These early results are extended to incorporate the notions of fairness [22] and partial order reduction [25] and an on the y extension is introduced [36] Symmetries in logical subformulas are exploited [2, 50] in LTL and CTL respectively. Symmetry reductions have been implemented within ....

E.M. Clarke, E.A. E.M. Emerson, S. Jha, and A.P. Sistla. Symmetry reductions in modelchecking. In [39], pp. 147-158, 1998.

....part of the state space is represented during the analysis, because there is no need in general to construct rst the whole state space and then traverse it. Last but not least some techniques involving reducing the statespace using symmetry arguments have been proposed and successfully used, see [9]. All these techniques could be equally applied to our diconnected components approach, and should be exempli ed in future papers. For instance, symmetry techniques are quite well studied in geometry and should apply straightforwardly to our geometric approach. 8 Concluding remarks Two further ....

E. M. Clarke, E. A. Emerson, S. Jha, and A. P. Sistla. Symmetry reductions in model checking. In Proc. 10th International Computer Aided Veri cation Conference, pages 145-458, 1998.

....of memory is used when the search is finished. But the execution time is considerably reduced, because it is not necessary to put a copy of the state on the stack anymore. 2. 4 Exploiting Symmetries Symmetries have been used in model checking to reduce the size of the state space [EJ93,ID96,CEJS98,CFJ93,BDH00] The basic idea is to visit a subset of the state space that is representative of the whole state space based on a symmetry relation that does not influence the properties being checked. Typically symmetry reductions exploit the structure of the system being analyzed, e.g. identical ....

....whenever a state is generated we calculate a canonical representation of the state and use this representation for state comparisons. The use of a canonization function is a well known technique for achieving symmetry reductions [BDH00,ID96] but calculating this function can be very expensive [CEJS98] in itself. However, since we are only interested in a limited form of symmetry reduction, we can calculate the canonical state representation very efficiently by imposing an order on the entries in the static and dynamic areas. Due to the dynamic nature of Java programs, this ordering must be ....

Edmund M. Clarke, E. Allen Emerson, Somesh Jha, and A. Prasad Sistla. Symmetry reductions in model checking. In Proc. of the 10th International Conference on Computer Aided Verification, volume 1427 of LNCS, pages 147--158. Springer-Verlag, 1998.

.... of the state space, the state space size often grows exponentially with the size of the description of the model (usually given in the form of a program in some computer language) Despite various symbolic representation techniques using BDDs [12] and their numerous variants, symme# try reduction [17], modular decomposition [62] breadth first checking with the SAT procedure [9] etc. model checking still has to scale up for hardware, not speaking of software. Di#culties also come out of the temporal logic used for the specification which is often beyond human understanding capabilities [64 , ....

E.M. Clarke, E.A. Emerson, S. Jha, and A.P. Sistla. Symmetry reductions in model checking. In A.J. Hu and M.Y. Vardi, eds., Proc. 10 Int. Conf. CAV ' 98 , Vancouver, BC, CA,LNCS 1427, pages 147--158. Springer-Verlag, 28 June -- 2 Jul. 1998.

....non trivial symmetries grows double exponentially. On the other hand, for a function with exponentially many symmetries, trying to explicitly use all symmetries may defeat the purpose of speeding up search [18] Despite these pitfalls, symmetry based approaches have been useful in model checking [26, 15, 23], hardware verification [36] software verification [11] logic synthesis [28, 9] and DSP algorithms [22] Some researchers limited the notion of symmetry to swaps of variables [22] or subsets of variables [28] to achieve efficiency. Other works [9, 44] limited the notion of symmetry to negations ....

E.M. Clarke et al., (Edited by: Hu, A.J.; Vardi, M.Y.) "Symmetry Reductions in Model Checking", in Intl. Conf. Computer Aided Verification (CAV) '98, pp. 159-171.

.... semantic symmetries versus syntactic symmetries that leave the CNF formula unchanged. The empirical data in [11, Figure 3] does not appear consistent with this suggestion. To this end, 16] demonstrated large numbers of symmetries in Boolean functions from synthesis applications. ing [15, 9], verification [19] synthesis of logic circuits [17] and DSP algorithms [13] In this work, we propose a completely automated flow that: # starts with a CNF formula in the DIMACS format, # detects all of its symmetries (not just pairwise swaps) # represents all symmetries implicitly and ....

E.M. Clarke et al., (Edited by: Hu, A.J.; Vardi, M.Y.) "Symmetry Reductions in Model Checking", CAV'98, pp.159-71.

....richer symmetries. Indeed, Boolean functions from synthesis applications may have many symmetries [14] If exponentially many symmetries exist, adding all possible symmetry breaking clauses can be disastrous [9] Despite these pitfalls, symmetry based approaches have been useful in model checking [13, 7], verification [16] logic synthesis [15] and DSP algorithms [11] In this work, we propose an automated flow that starts with a CNF formula in the DIMACS format and detects all of its symmetries (not just pairwise swaps) In this flow, all symmetries are captured implicitly, with exponential ....

E.M. Clarke et al., (Edited by: Hu, A.J.; Vardi, M.Y.) "Symmetry Reductions in Model Checking", CAV'98, pp.159-71.

.... have been proposed which make use of such high level information and which are based on word level verification techniques, like for example Word Level Decision Diagrams (e.g. 8] formal Bitvector Theories (e.g. 1, 6] Integer Linear Programming (e.g. 14] Symmetry Reductions (e.g. [4, 9]) and Term Rewriting (e.g. 7] to survey only a few. 2 Scaling Design Sizes before Verification This paper presents a new word level abstraction technique which is used as a preprocess in high level property checking of digital circuits. The proposed method automatically scales down data path ....

....We write x [n] i] to refer to the i th bit of the value of x [n] The set of well formed L(Bv) terms is defined inductively over a finite set of bitvector variables and the set of bitvector operators shown in Table 1. Operator Syntax Example bitvector variables x [n] x [8] y [16] z [4] ; bitvector constants vn 1 : v 1 v0 0000; 1111; 00101011; concatenation x [16] y [12] z [4] extraction [j; i] x [4] y [32] 5; 2] bitwise negation neg x [8] neg(y [8] bitwise Boolean and; or; xor x [16] y [16] and z [16] connectives nand; nor; xnor x [16] y [16] or ....

[Article contains additional citation context not shown here]

E. M. Clarke, E. A. Emerson, S. Jha, and A. P. Sistla. "Symmetry Reductions in Model Checking". In Proc. CAV, pages 147--158, 1998.

....of memory is used when the search is finished. But the execution time is considerably reduced, because it is not necessary to put a copy of the state on the stackanymore. 2. 4 Exploiting Symmetries Symmetries have been used in model checking to reduce the size of the state space [EJ93] ID96] CEJS98] CFJ93] BDH00] The basic idea is to visit a subset of the state space that is representative of the whole state space based on a symmetry relation that does not influence the properties being checked. Typically symmetry reductions exploit the structure of the system being analyzed, e.g. ....

....whenever a state is generated calculate a canonical representation of the state and use this representation for state comparisons. The use of a canonization function is a well known technique for achieving symmetry reductions [BDH00] ID96] but calculating this function can be very expensive [CEJS98] in itself. However, since we are only interested in a limited form of symmetry reduction, we can calculate the canonical state representation very efficiently by imposing an order on the entries in the static and dynamic area. Due to the dynamic nature of Java programs, this ordering must be ....

Edmund M. Clarke, E. Allen Emerson, Somesh Jha, and A. Prasad Sistla. Symmetry reductions in model checking. In Proc. of the 10th International Conference on Computer Aided Verification,volume 1427 of LNCS, pages 147--158. Springer-Verlag, 1998.

....of orbit problems in case a group is acting on strings, permuting the element positions. This kind of string orbit problems are, for instance, in the core of symmetry reduction methods designed to alleviate the state space explosion problem appearing in the analysis of concurrent systems [5, 7, 4]. They also arise in the enumeration of combinatorial objects such as block designs, see e.g. 6] First, for the sake of completeness, we restate a result by Clarke et al. 4] the problem of deciding whether two strings are equivalent under the action of a group (i.e. belong to the same orbit) ....

.... methods designed to alleviate the state space explosion problem appearing in the analysis of concurrent systems [5, 7, 4] They also arise in the enumeration of combinatorial objects such as block designs, see e.g. 6] First, for the sake of completeness, we restate a result by Clarke et al. [4]: the problem of deciding whether two strings are equivalent under the action of a group (i.e. belong to the same orbit) is polynomial time many one equivalent to the problem of deciding whether a coset has a stabilizer for a set. This problem is polynomial time equivalent to many important ....

[Article contains additional citation context not shown here]

E. M. Clarke, E. A. Emerson, S. Jha, and A. P. Sistla. Symmetry reductions in model checking. In A. J. Hu and M. Y. Vardi, editors, Computer Aided Verification (CAV'98), volume 1427 of LNCS, pages 147--158. Springer, 1998.

....representing sets of states [2] When a state s 0 equivalent to s is visited later during the search, the search does not explore successors of s 0 . Various schemes have been proposed for efficiently implementing canonicalization functions [17] The complexity of this problem is discussed in [4]. 4 SYMMETRY ON TRANSITIONS Storing states in memory in one form (hash table) or another (BDDs) and using canonicalization functions assumes that every system state can easily be encoded by a unique string of bits. When dealing with processes described by arbitrary programs written in ....

E. M. Clarke, E. A. Emerson, S. Jha, and A. P. Sistla. Symmetry Reductions in Model Checking. In Proc. 10th Conference on Computer Aided Verification, volume 1427 of Lecture Notes in Computer Science, pages 147--158, Vancouver, June/July 1998. Springer-Verlag.

....same complexity as classical BDD algorithms but the algorithms for the determination of logical functions have to be changed and become more complicated. BDDs appearing in different layers cannot be shared and the method is only suitable for hierarchical systems. Symmetry and abstraction: Symmetry [9, 7] and abstraction [8] are very powerful methods to reduce the necessary resources for the verification of a system. The problem is that it has to be proven manually that the application of a certain abstraction or symmetry relation preserves the correctness of the verification. To exploit symmetry, ....

E. M. Clarke, E. A. Emerson, and A. P. Sistla. Symmetry reductions in model checking. In Computer Aided Verification, 10th International Conference, CAV'98, volume 1427 of Lecture Notes in Computer Sciences, pages 147--158, 1998.

....a symmetry sub group Sym(G) it is su cient to inspect only one representative of each equivalence class ( orbit) of states during the reachability analysis. Thus a reduced reachability graph can be generated and substantial savings achieved both in the time and memory requirements (see e.g. [5, 17, 18, 25]) The properties that one is able to check from reduced reachability graphs range from simple deadlock absence, safety and Petri net speci c properties [3, 4, 15, 17, 18] to full edged model checking of temporal logic formulae [1, 6, 7, 8, 12] As the generation of the full reachability graph is ....

.... mentioned in the beginning of this section) For detailed reachability graph generation algorithm descriptions see e.g. 6, 7, 17, 18, 27] For complexity results concerning the orbit problem (are two states in the same orbit, calculation of the canonical representative state) refer, e.g. to [5, 6, 17]. During the example we have actually found and utilized the symmetry generating information of the nets. For the P T net the generating group is the internal direct product of the permutation groups 1 and 2 , where 1 is the set of all rotation permutations of the net respecting node types ....

[Article contains additional citation context not shown here]

E. M. Clarke, E. A. Emerson, S. Jha, and A. P. Sistla. Symmetry reductions in model checking. In Hu and Vardi [13], pages 147-158.

....structure M(P ) is bisimilar up to permutation to M(P ) jSym I . For the future, we plan on implementing a preprocessor front end to a symbolic model checking tool to take advantage of our results on full symmetry. We are also investigating extending our technique to a larger class of groups [CEJS98] for which symmetry reduction can be applied directly to program text. With respect to near symmetry and full symmetry we are interested in exploring the applicability of our work here to symmetry reduction techniques which use the annotated symmetry reduced structure which preserves the truth of ....

Clarke, E. M., Emerson, E. A., Jha, S. and Sistla A. P., Symmetry Reductions in Model Checking. In Computer Aided Verification, 10th International Conference LNCS 1427, Springer- Verlag, 1998.

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Clarke, E. M., Emerson, E. A., Jha, S. and Sistla A. P., Symmetry Reductions in Model Checking. In Computer Aided Verification, 10th International Conference LNCS 1427, Springer- Verlag, 1998.

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E. M. Clarke et al., "Symmetry reductions in model checking," in Proc. Int. Conf. Computer-Aided Verification, A. J. Hu and M. Y. Vardi, Eds., 1998, pp. 159--171.

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E. Clake, E.A. Emerson, S. Jha, and A.P. Sistla, \Symmetry Reductions in Model Checking," in Proceedings of CAV'98. 1998, vol. 1427 of LNCS, pp. 147-159, Springer-Verlag.

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E. Clake, E.A. Emerson, S. Jha, and A.P. Sistla, Symmetry Reductions in Model Checking, Proc. of CAV'98, LNCS, vol. 1427, Springer-Verlag, 1998, pp. 147--159.

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