I-H. Moon, G. D. Hachtel, and F. Somenzi. Border-block triangular form and conjunction schedule in image computation. In W. A. Hunt, Jr. and S. D. Johnson, editors, Formal Methods in Computer Aided Design, pages 73--90. Springer-Verlag, November 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....area in the mid 90s, see for example [1, 2] the researchers concentrated on other topics of the reachability analysis galaxy, namely approximate reachability analysis, guided traversal, etc. Only recently the question of image computation gained again the attention of the scientific community [3,4,5,6,7]. We basically follow this recent trend and we try to further optimize image computation introducing an approach based on dynamic sorting, dynamic clustering and partitioning. We start from an ordering technique derived from [1] but with major modifications introduced keeping into account the ....

....mix the technique just presented, based on the transition relation, and the one based on recursive case splitting, often known as transition function. They show that very often one technique outperforms the other and propose a hybrid approach based on an on the fly selection of the method. In [4] the authors try to produce a good quantification schedule minimizing the active lifetime of variables, i.e. the number of conjunctions in which the variable participate. The method is based on the analysis and manipulation of the dependence matrix of the system, i.e. the matrix that indicates ....

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I. H. Moon and F. Somenzi. Border-Block Triangular Form and Conjunction Schedule in Image Conjunction. In Proc. Formal Methods in Computer-Aided Design, volume 1954.

....proper cluster size thresholds (in the range from ### to #### BDD nodes) We enable dynamic reordering (group sifting with groups made up of corresponding present next state variables) with the default settings of the CUDD package. Table 1 compares standard breadth first implementation [10], the profile based technique [6] the distance driven based technique [8] and the proposed method. In [10] authors analyze standard breadth first traversal focusing on a new clustering algorithm, where the clusters and their order are evaluated based on the dependence matrix of the ....

....sifting with groups made up of corresponding present next state variables) with the default settings of the CUDD package. Table 1 compares standard breadth first implementation [10] the profile based technique [6] the distance driven based technique [8] and the proposed method. In [10] authors analyze standard breadth first traversal focusing on a new clustering algorithm, where the clusters and their order are evaluated based on the dependence matrix of the transition relation. Results are obtained using a ### MHz Pentium II Workstation running Linux. The memory limit in this ....

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I. Moon and F. Somenzi. Border-Block Triangular Form and Conjunction Schedule in Image Conjunction. In Proc. FMCAD'00, To Appear, 2000.

....Part of the reason for this, ironically, is the fact that it is in general not feasible to construct a single BDD for R. Instead, R is represented as the conjunction of several BDDs. The problem then arises how to compute EX(Q) without actually computing R. In a recent series of papers [7, 26, 27], improved algorithms for image computation have been investigated. Theoretical Limitations of Symbolic Model Checking. Potentially, the BDD representation of a Kripke structure may be exponentially more succinct than the explicit representation. Practical experience with symbolic verification ....

I. Moon and F. Somenzi. Border-block triangular form and conjunction schedule in image computation. In Proceedings of the Formal Methods in Computer Aided Design (FMCAD '00), November 2000. To appear.

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I-H. Moon, G. D. Hachtel, and F. Somenzi. Border-block triangular form and conjunction schedule in image computation. In W. A. Hunt, Jr. and S. D. Johnson, editors, Formal Methods in Computer Aided Design, pages 73--90. Springer-Verlag, November 2000.

....between normalization and parameterization. Experimental results are shown in Section 9 and we conclude with Section 10. 2 Preliminaries Image computation is finding all successor states from a given set of states in one step and is a key step in model checking to deal with sequential circuits [15, 17, 16]. Let x and y be the sets of present and next state variables and w be the set of primary input variables. Suppose we have a transition relation T (x; w; y) that represents all transitions, being true of just those triples of a, b, and c, such that there is a transition from state a to state c, ....

I.-H. Moon, G. D. Hachtel, and F. Somenzi. Border-block triangular form and conjunction schedule in image computation. In W. A. Hunt, Jr. and S. D. Johnson, editors, Formal Methods in Computer Aided Design, pages 73--90. Springer-Verlag, November 2000.

....at a time, still, using the same quality measure as we did in the previous step. This step requires more computations than the previous one. Heuristic 3. If we fail to nd any group through the previous steps, we transform a support matrix using the MLP (Minimal Lifetime Permutation) technique [12] to a lower triangularized form, and group identi cation is attempted. As an example, we show a triangularized support matrix on the right in Figure 4, which is transformed from the one on the left. 0 1 2 3 4 5 0 1 2 3 B B B 1 1 1 1 1 1 1 C C C 0 1 3 4 5 2 1 3 2 0 B B B 1 ....

....a ect the hardness signi cantly. Moon et al. proposed the use of variable lifetimes in the dependence matrix [13] Also Moon et al. proposed the MLP (Minimal Lifetime Permutation) method to get a good quanti cation schedule by trying to decrease variable lifetime by using the dependence matrix [12]. We use the variable lifetime in the MLP method to see whether there is a good quanti cation schedule for Q. For this purpose, we rst take an initial matrix to contain only the variables KG and QG of the group G. Then we perform the MLP method and we compute the variable lifetime with respect ....

I.-H. Moon, G. D. Hachtel, and F. Somenzi. Border-block triangular form and conjunction schedule in image computation. In W. A. Hunt, Jr. and S. D. Johnson, editors, Formal Methods in Computer Aided Design, pages 73-90. Springer-Verlag, Nov. 2000.

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I.-H. Moon, G. D. Hachtel, and F. Somenzi, "Border-block triangular form and conjunction schedule in image computation," in Formal Methods in Computer-Aided Design, Nov. 2000.

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I.-H. Moon, G. D. Hachtel, and F. Somenzi, "Border-block triangular form and conjunction schedule in image computation," in Formal Methods in Computer-Aided Design, Nov. 2000.

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In-Ho Moon, Gary D. Hachtel, and Fabio Somezni. Border-Block Triangular Form and Conjunction Schedule in Image Computation. In 3rd Internation Conference on Formal Methods in Computer Aided Design (FMCAD'00), pages 73--90, 2000.

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In-Ho Moon and Fabio Somenzi. Border-Block Triangular Form and Conjunction Schedule in Image Computation. In Proceedings of the Formal Methods in Computer Aided Design (FMCAD), November 2000.

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