Abstract
We present a sound static analysis technique for fighting the combinatorial explosion of parameterised Boolean equation systems (PBESs). These essentially are systems of mutually recursive fixed point equations ranging over first-order logic formulae. Our method detects parameters that are not live by analysing a control flow graph of a PBES, and it subsequently eliminates such parameters. We show that a naive approach to constructing a control flow graph, needed for the analysis, may suffer from an exponential blow-up, and we define an approximate analysis that avoids this problem. The effectiveness of our techniques is evaluated using a number of case studies.
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
Aho, A.V., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques, and Tools. Addison-Wesley (1986)
Alpuente, M., Feliú, M.A., Joubert, C., Villanueva, A.: Datalog-based program analysis with BES and RWL. In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds.) Datalog 2010. LNCS, vol. 6702, pp. 1–20. Springer, Heidelberg (2011)
Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL 1977, pp. 238–252. ACM, New York (1977)
Cranen, S., Groote, J.F., Keiren, J.J.A., Stappers, F.P.M., de Vink, E.P., Wesselink, W., Willemse, T.A.C.: An overview of the mCRL2 toolset and its recent advances. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 199–213. Springer, Heidelberg (2013)
Fernandez, J.-C., Bozga, M., Ghirvu, L.: State space reduction based on live variables analysis. Science of Computer Programming 47(2-3), 203–220 (2003)
Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2010: A toolbox for the construction and analysis of distributed processes. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 372–387. Springer, Heidelberg (2011)
Groote, J.F., Willemse, T.A.C.: Parameterised boolean equation systems. Theoretical Computer Science 343(3), 332–369 (2005)
Hesselink, W.H.: Invariants for the construction of a handshake register. Information Processing Letters 68, 173–177 (1998)
Keiren, J.J.A., Wesselink, J.W., Willemse, T.A.C.: Improved static analysis of parameterised boolean equation systems using control flow reconstruction. arXiv:1304.6482 [cs.LO] (2013)
Mader, A.: Verification of Modal Properties Using Boolean Equation Systems. PhD thesis, Technische Universität München (1997)
Mateescu, R.: Vérification des propriétés temporelles des programmes parallèles. PhD thesis, Institut National Polytechnique de Grenoble (1998)
Orzan, S., Wesselink, W., Willemse, T.A.C.: Static Analysis Techniques for Parameterised Boolean Equation Systems. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 230–245. Springer, Heidelberg (2009)
Ploeger, B., Wesselink, W., Willemse, T.A.C.: Verification of reactive systems via instantiation of parameterised Boolean equation systems. Information and Computation 209(4), 637–663 (2011)
van de Pol, J., Timmer, M.: State Space Reduction of Linear Processes Using Control Flow Reconstruction. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 54–68. Springer, Heidelberg (2009)
Willemse, T.A.C.: Consistent Correlations for Parameterised Boolean Equation Systems with Applications in Correctness Proofs for Manipulations. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 584–598. Springer, Heidelberg (2010)
Yorav, K., Grumberg, O.: Static Analysis for State-Space Reductions Preserving Temporal Logics. Formal Methods in System Design 25(1), 67–96 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Keiren, J.J.A., Wesselink, W., Willemse, T.A.C. (2014). Liveness Analysis for Parameterised Boolean Equation Systems. In: Cassez, F., Raskin, JF. (eds) Automated Technology for Verification and Analysis. ATVA 2014. Lecture Notes in Computer Science, vol 8837. Springer, Cham. https://doi.org/10.1007/978-3-319-11936-6_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-11936-6_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11935-9
Online ISBN: 978-3-319-11936-6
eBook Packages: Computer ScienceComputer Science (R0)