Abstract
Symbolic state space traversal techniques are one of the most notable achievements in the fields of formal verification and of automated synthesis. Transition functions and transition relations are two alternative approaches. In terms of efficiency, transition functions have proven to be superior, although the transition relation is much more expressive. This paper brings the transition relation back to a new life, profiting from recent advancements in the fields of boolean function representation, simplification, and image computation represented by BDDs and by the generalized cofactor operator. A theoretical result allows us to considerably simplify both the process of building the transition relation and of traversing the state space. Experimental results show that performances similar to those of the transition function are obtained.
This work has been partially supported by the ESPRIT Working Group 6018 “CHARME-2”.
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References
Brglez, F. Bryan, D., Koźmiński, K.: Combinatorial Profiles of Sequential Benchmark Circuits. ISCAS'89: IEEE Int'l Symposium on Circuits and Systems, Portland, OR (USA), May 1989, pp. 1929–1934
Burch, J.R., Clarke, E.M., Long, D.E.: Representing Circuits More Efficiently in Symbolic Model Checking. DAC'91: 28th ACM/IEEE Design Automation Conference, San Francisco, CA (USA), June 1991, pp. 403–407
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic Model Checking: 1020 States and Beyond. LICS'90: 5th Annual IEEE Symposium on Logic in Computer Science, June 1990, pp. 428–439
Bochmann, D., Dreisig, F., Steinbach, B.: A new Decomposition Method for Multilevel Circuit Design. EDAC'91: IEEE European Conference on Design Automation, Amsterdam (The Netherlands), February 1991, pp. 374–377
Brace, K.S., Rudell, R.L., Bryant, R.E.: Efficient Implementation of a BDD Package. DAC'90: 27th ACM/IEEE Design Automation Conference, Orlando, FL (USA), June 1990, pp. 40–45
Bryant, R.E.: Graph-based Algorithms for Boolean Function Manipulation. IEEE Transactions on Computer, Vol. C-35, No. 8, August 1986, pp. 677–691
Coudert, O., Berthet, C., Madre, J.C.: Verification of Sequential Machines Based on Symbolic Execution. “Automatic verification methods for finite state systems,”, J. Sifakis editor, Lecture Notes in Computer Science 407, Springer Verlag, Berlin (Germany), 1989, pp. 365–373
Coudert, O., Berthet, C., Madre, J.C.: Verification of Sequential Machines Using Boolean Function Vectors. IFIP Int'l Workshop on “Applied Formal Methods for Correct VLSI Design”, Leuven (Belgium), November 1989, Vol. 1, pp. 111–128
Cabodi, G.P., Camurati, P., Corno, F., Gai, S., Prinetto, P., Sonza Reorda, M.: A new Model for Improving Symbolic Product Machine Traversal. DAC-29: 29th ACM/IEEE Desing Automation Conference, Anaheim, CA (USA), June 1992, pp. 614–619
Camurati, P., Corno, F., Prinetto, P.: Exploiting symbolic traversal techniques for efficient Process Algebra Manipulation. CHDL'93: IFIP Conference on Hardware Description Languages and their Applications, Ottawa (Canada), April 1993
Cho, H., Hachtel, G., Jeong, S.W., Plessier, B., Schwarz, E., Somenzi, F.: ATPG Aspects of FSM Verification. ICCAD-90: IEEE Int'l Conference on Computer Aided Design, Santa Clara, CA (USA), November 1990, pp. 134–137
Coudert, O., Madre, J.C.: A Unified Framework for the Formal Verification of Sequential Circuits. ICCAD-90: IEEE Int'l Conf. on Computer Aided Design, Santa Clara, CA (USA), November 1990, pp. 126–129
Coudert, O., Madre, J.C.: Symbolic Computation of the Valid States of the Sequential Machine: Algorithms and Discussion. 1991 Int'l Workshop on Formal Methods in VLSI Design, Miami, FL (USA), January 1991
Enders, R., Filkorn, T., Taubner, D.: Generating BDDs for Symbolic Model Checking in CCS. CAV'91: Computer-Aided Verification Workshop, Aalborg (Denmark), July 1991, K.G. Larsen, A. Skou Editors, Lecture Notes in Computer Science 575, Springer Verlag, Berlin (Germany), pp. 203–213
Kohavi, Z.: Switching and Finite Automata Theory, second edition, Computer Science Series, Mc Graw Hill, New York, NY
Touati, H., Savoj, H., Lin, B., Brayton, R.K., Sangiovanni-Vincentelli, A.: Implicit Enumeration of Finite State Machines Using BDDs. ICCAD-90: IEEE International Conference on Computer Aided Design, Santa Clara, CA (USA), November 1990, pp. 130–133
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Cabodi, G., Camurati, P. (1993). Advancements in symbolic traversal techniques. In: Milne, G.J., Pierre, L. (eds) Correct Hardware Design and Verification Methods. CHARME 1993. Lecture Notes in Computer Science, vol 683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021721
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DOI: https://doi.org/10.1007/BFb0021721
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