Abstract
We introduce a class of computational problems called the partial order constraint satisfaction problems (POCSPs) and present three methods for encoding them as binary decision diagrams (BDDs). The first method, which simply augments domain constraints with the transitivity and asymmetry for partial orders, is improved by the second method, which introduces the notion of domain variables to reduce the number of Boolean variables. The third method turns out to be most useful for monotonic domain constraints, because it requires no explicit encoding for the transitivity. We show how those methods are successfully applied to expert systems in a software verification domain.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Akers, S.B.: Binary decision diagrams. IEEE Trans. Comput. C-27(6), 509–516 (1978)
Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Trans. on Computers 45, 993–1002 (1996)
Bryant, R.E.: Graph-based algorithm for boolean function manipulation. IEEE Trans. Comput. C-35(5), 677–691 (1986)
Coudert, O., Madre, J.C.: Towards an interactive fault tree analyser. In: Proc. IASTED Int. Conf. on Reliability, Quality Control and Risk Assessment (1992)
Dershowitz, N., Jouannaud, J.-P.: Rewrite Systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 243–320. North-Holland, Amsterdam (1990)
Detlefs, D., Forgaad, R.: A procedure for automatically proving the termination of a set of rewrite rules. In: Jouannaud, J.-P. (ed.) RTA 1985. LNCS, vol. 202, pp. 255–270. Springer, Heidelberg (1985)
Fujita, M., Fujisawa, H., Matsunaga, Y.: Variable ordering algorithms for ordered binary decision diagrams and their evaluation. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 12, 6–12 (1993)
Kurihara, M., Kondo, H., et al.: Using ATMS to efficiently verify the termination of rewrite rule programs, Intern. Journal of Software Engineering and Knowledge Engineering 2(4), 547–565 (1992)
Madre, J.C., Coudert, O.: A logically complete reasoning maintenance system based on a logical constraint solver. In: Proc. Intern. Joint Conf. on Artificial Intelligence, pp. 294–299 (1991)
Malik, S., et al.: Logic verification using binary decision diagrams in a logic synthesis environment. In: Proc. IEEE Int. Conf. on Computer-Aided Design, pp. 6–9 (1988)
Minato, S., Ishiura, N., Yajima, S.: Shared binary decision diagram with attributed edges for efficient Boolean function manipulation. In: 27th DAC, pp. 52–57 (1990)
Moore, J.S.: Introduction to the OBDD algorithm for the ATP community. Journal of Automated Reasoning 12, 33–45 (1994)
Plaisted, D.A.: Equational reasoning and term rewriting systems. In: Gabbay, D.M. (ed.) Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 274–364 (1993)
Sieling, D.: On the existence of polynomial time approximation schemes for OBDD minimization. In: Meinel, C., Morvan, M. (eds.) STACS 1998. LNCS, vol. 1373, pp. 205–215. Springer, Heidelberg (1998)
Steinbach, J.: Termination of rewriting: Ph.D thesis, Univ. Kaiserslautern, Germany (1994)
Steinbach, J., Kühler, U.: Check your ordering: termination proofs and open problems, SEKI report SR-90-25(SFB), Univ. Kaiserslautern, Germany (1990)
Tani, S., Hamaguchi, K., Yajima, S.: The complexity of the optimal variable ordering problem of a shared binary decision diagram. In: Ng, K.W., Balasubramanian, N.V., Raghavan, P., Chin, F.Y.L. (eds.) ISAAC 1993. LNCS, vol. 762, pp. 389–398. Springer, Heidelberg (1993)
Wegener, I.: Branching Programs and Binary Decision Diagrams: Theory and Application. Society for Industrial and Applied Mathematics (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kurihara, M., Kondo, H. (2004). Efficient BDD Encodings for Partial Order Constraints with Application to Expert Systems in Software Verification. In: Orchard, B., Yang, C., Ali, M. (eds) Innovations in Applied Artificial Intelligence. IEA/AIE 2004. Lecture Notes in Computer Science(), vol 3029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24677-0_85
Download citation
DOI: https://doi.org/10.1007/978-3-540-24677-0_85
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22007-7
Online ISBN: 978-3-540-24677-0
eBook Packages: Springer Book Archive