Abstract
This work introduces a new data structure, called Lattice-Valued Binary Decision Diagrams (or LVBDD for short), for the compact representation and manipulation of functions of the form \(\theta : 2^{\tt P}\) ↦ \({\mathcal L}\), where P is a finite set of Boolean propositions and \({\mathcal L}\) is a finite distributive lattice. Such functions arise naturally in several verification problems. LVBDD are a natural generalisation of multi-terminal ROBDD which exploit the structure of the underlying lattice to achieve more compact representations. We introduce two canonical forms for LVBDD and present algorithms to symbolically compute their conjunction, disjunction and projection. We provide experimental evidence that this new data structure can outperform ROBDD for solving the finite-word LTL satisfiability problem.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Work supported by the projects: (i) Quasimodo: “Quantitative System Properties in Model-Driven-Design of Embedded System”, http://www.quasimodo.aau.dk/ , (ii) Gasics: “Games for Analysis and Synthesis of Interactive Computational Systems”, http://www.ulb.ac.be/di/gasics/ , (iii) Moves: “Fundamental Issues in Modelling, Verification and Evolution of Software”, http://moves.ulb.ac.be , a PAI program funded by the Federal Belgian Government, (iv) CFV (Federated Center in Verification) funded by the FNRS http://www.ulb.ac.be/di/ssd/cfv/
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: DAC 1993. ACM, New York (1993)
Reif Andersen, H., Hulgaard, H.: Boolean Expression Diagrams. In: LICS. IEEE, Los Alamitos (1997)
Devereux, B., Chechik, M.: Edge-Shifted Decision Diagrams for Multiple-Valued Logic. In: JMVLSC. Old City Publishing (2003)
Cousot, P., Cousot, R.: Abstract Interpretation: A Unified Lattice Model for Static Analysis of Programs by Construction or Approximation of Fixpoints. In: POPL 1977. ACM, New York (1977)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)
Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, J.: Symbolic Model Checking: 1020 States and Beyond. In: LICS 1990. IEEE, Los Alamitos (1990)
Chechik, M., Devereux, B., Easterbrook, S., Lai, A., Petrovykh, V.: Efficient Multiple-Valued Model-Checking Using Lattice Representations. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, p. 441. Springer, Heidelberg (2001)
Cimatti, A., Clarke, E.M., Giunchiglia, F., Roveri, M.: NuSMV: A new symbolic model verifier. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 495–499. Springer, Heidelberg (1999)
Delzanno, G., Raskin, J.-.F., Van Begin, L.: Covering sharing trees: a compact data structure for parameterized verification. In: STTT, vol. 5(2-3). Springer, Heidelberg (2003)
Bryant, R.: Graph-based Algorithms for Boolean Function Manipulation. IEEE Trans. on Comp. C-35(8) (1986)
Kupferman, O., Lustig, Y.: Lattice Automata. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 199–213. Springer, Heidelberg (2007)
Fujita, M., McGeer, P.C., Yang, J.C.Y.: Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Form. Methods Syst. Des. 10(2-3) (1997)
De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.F.: Antichains: A new algorithm for checking universality of finite automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006)
Doyen, L., Raskin, J.F.: Antichain Algorithms for Finite Automata. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 2–22. Springer, Heidelberg (2010)
Rozier, K., Vardi, M.: LTL Satisfiability Checking. In: Bošnački, D., Edelkamp, S. (eds.) SPIN 2007. LNCS, vol. 4595, pp. 149–167. Springer, Heidelberg (2007)
Geldenhuys, J., Hansen, H.: Larger automata and less work for LTL model checking. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 53–70. Springer, Heidelberg (2006)
Birkhoff, G.: Lattice Theory. Colloquim Publications. Am. Math. Soc., Providence (1999)
Lind-Nielsen, J.: Buddy: BDD package, http://www.itu.dk/research/buddy
NuSMV Model-checker, http://nusmv.irst.itc.it/
SMV Model-checker, http://www.cs.cmu.edu/~modelcheck/smv.html
Somenzi, F.: BDD package CUDD, http://vlsi.colorado.edu/~fabio/CUDD/
Ganty, P., Maquet, N., Raskin, J.F.: Fixpoint Guided Abstraction Refinements for Alternating Automata. In: Maneth, S. (ed.) CIAA 2009. LNCS, vol. 5642, pp. 155–164. Springer, Heidelberg (2009)
De Wulf, M., Doyen, L., Maquet, N., Raskin, J.F.: Antichains: Alternative Algorithms for LTL Satisfiability. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 63–77. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Geeraerts, G., Kalyon, G., Le Gall, T., Maquet, N., Raskin, JF. (2010). Lattice-Valued Binary Decision Diagrams. In: Bouajjani, A., Chin, WN. (eds) Automated Technology for Verification and Analysis. ATVA 2010. Lecture Notes in Computer Science, vol 6252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15643-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-15643-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15642-7
Online ISBN: 978-3-642-15643-4
eBook Packages: Computer ScienceComputer Science (R0)