Abstract
Multiway Decision Graphs (MDGs) are a canonical representation of a subset of many-sorted first-order logic. It generalizes classical BDDs with abstract data and uninterpreted functions. In this paper, we describe a new MDG construction based on the Generalized-If-Then-Else (GITE) operator. Consequently, we review the main algorithms used for verification techniques i.e. relational product and pruning by subsumption. Unlike an earlier version of the MDG package, basic MDG algorithms are defined uniformly through this single GITE operator which will lead to a more efficient implementation. The new tool, called NuMDG, accepts an extended SMV language, supporting abstract data sorts.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bryant, R.E.: Graph-based Algorithms for Boolean Function Manipulation. IEEE Transactions on Computers 35(8), 677–691 (1986)
Corella, F., Zhou, Z., Song, X., Langevin, M., Cerny, E.: Multiway Decision Graphs for Automated Hardware Verification. Formal Methods in System Design 10(2), 7–46 (1997)
Tahar, S., Song, X., Cerny, E., Zhou, Z., Langevin, M., Ait Mohamed, O.: Modeling and Verification of the Fairisle ATM Switch Fabric using MDGs. IEEE Transactions on CAD of Integrated Circuits and Systems 18(7), 956–972 (1999)
Xu, Y., Cerny, E., Song, X., Corella, F., Ait Mohamed, O.: Model Checking for A First-Order Temporal Logic using Multiway Decision Graphs. The Computer Journal 47(1), 71–84 (2004)
Zhou, Z.: Mutliway Decision Graphs and Their Applications in Automatic Formal Verification of RTL Designs, PhD thesis, Montréal University (1997)
Burch, J.R., Dill, D.L.: Automatic Verification of Pipelined Microprocessor Control. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 68–80. Springer, Heidelberg (1994)
Damm, W., Pnueli, A., Ruah, S.: Herbrand Automata for Hardware Verification. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 67–83. Springer, Heidelberg (1998)
Berezin, S., Biere, A., Clarke, E.M., Zhu, Y.: Combining Symbolic Model Checking with Uninterpreted Functions for Out-of-Order Processor Verification. Formal Methods in Computer Aided Design 1522, 187–201 (1998)
Hojati, R., Kuehlmann, A., German, S., Brayton, R.K.: Validity Checking in the Theory of Equality with Uninterpreted Functions using Finite Instantiations. In: The International Workshop on Logic Synthesis (1997)
Goel, A., Sajid, K., Zhou, H., Aziz, A., Singhal, V.: BDD based Procedures for A Theory of Equality with Uninterpreted Functions. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 244–255. Springer, Heidelberg (1998)
Bryant, R.E., German, S., Velev, M.N.: Processor Verification Using Efficient Reductions of the Logic of Uninterpreted Functions to Propositional Logic. ACM Transactions on Computational Logic 2(1), 93–134 (2001)
Ackermann, W.: Solvable Cases of the Decision Problem. North-Holland Pub. Co., Amsterdam (1954)
Pnueli, A., Rodeh, Y., Shitrichman, O., Siegel, M.: Deciding Equality Formulas by Small Domain Instantiations. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 455–469. Springer, Heidelberg (1999)
Velev, M.N.: Using Rewriting Rules and Positive Equality to Formally VerifyWide-issue Out-of-Order Microprocessors with Reorder Buffer. In: Proc. of DAC, pp. 28–35 (2002)
Clocksin, W., Mellish, C.: Programming in Prolog, 3rd edn. Springer, Heidelberg (1987)
Bahar, R., Frohm, E., Gaona, C., Hatchel, G., Macii, E., Pardo, A., Sommenzi, F.: Algebraic Decision Diagrams and their Applications. In: Proc. of International Conference on Computer-Aided Design, pp. 188–191 (1993)
Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV Version 2: An OpenSource Tool for Symbolic Model Checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, Springer, Heidelberg (2002)
Ait Mohamed, O., Song, X., Cerny, E.: On the Non-termination of MDG-based Abstract State Enumeration. Theoretical Computer Science 300, 161–179 (2003)
Mokhtari, Y., Abed, S., Ait Mohamed, O., Tahar, S., Song, X.: A New Approach for the Construction of Multiway Decision Graphs. Technical Report 2008-3-Abed, ECE Department, Concordia University, Montreal, Canada (June 2008)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mokhtari, Y., Abed, S., Ait Mohamed, O., Tahar, S., Song, X. (2008). A New Approach for the Construction of Multiway Decision Graphs. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds) Theoretical Aspects of Computing - ICTAC 2008. ICTAC 2008. Lecture Notes in Computer Science, vol 5160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85762-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-85762-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85761-7
Online ISBN: 978-3-540-85762-4
eBook Packages: Computer ScienceComputer Science (R0)