Abstract
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model checking. We consider models where the system state contains mutable function and predicate state variables. Such a model can describe systems containing arbitrarily large memories, buffers, and arrays of identical processes. We describe a form of predicate abstraction that constructs a formula over a set of universally quantified variables to describe invariant properties of the function state variables. We provide a formal justification of the soundness of our approach and describe how it has been used to verify several hardware and software designs, including a directory-based cache coherence protocol with unbounded FIFO channels.
This research was supported in part by the Semiconductor Research Corporation, Contract RID 1029.
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
Ball, T., Majumdar, R., Millstein, T., Rajamani, S.K.: Automatic predicate abstraction of C programs. In: Programming Language Design and Implementation (PLDI 2001), pp. 203–213 (2001)
Baukus, K., Lakhnech, Y., Stahl, K.: Parameterized Verification of a Cache Coherence Protocol: Safety and Liveness. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 317–330. Springer, Heidelberg (2002)
Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Springer, Heidelberg (1997)
Bryant, R.E., Lahiri, S.K., Seshia, S.A.: Modeling and verifying systems using a logic of counter arithmetic with lambda expressions and uninterpreted functions. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 78–92. Springer, Heidelberg (2002)
Chou, C.T.: The mathematical foundation fo symbolic trajectory evaluation. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 196–207. Springer, Heidelberg (1999)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for the static analysis of programs by construction or approximation of fixpoints. In: Principles of Programming Languages (POPL 1977), pp. 238–252 (1977)
Das, S., Dill, D.L.: Counter-example based predicate discovery in predicate abstraction. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 19–32. Springer, Heidelberg (2002)
Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: Launchbury, J., Mitchell, J.C. (eds.) Principles of Programming Languages (POPL 2002), pp. 191–202 (2002)
German, S.: Personal communication
Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)
Ip, C.N., Dill, D.L.: Verifying systems with replicated components in Murϕ. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 147–158. Springer, Heidelberg (1996)
Lahiri, S.K., Bryant, R.E., Cook, B.: A symbolic approach to predicate abstraction. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 141–153. Springer, Heidelberg (2003)
Lahiri, S.K., Seshia, S.A., Bryant, R.E.: Modeling and verification of out-of-order microprocessors in UCLID. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 142–159. Springer, Heidelberg (2002)
Lamport, L.: Anewsolution of Dijkstra’s concurrent programming problem. Communications of the ACM 17, 453–455 (1974)
Pnueli, A., Ruah, S., Zuck, L.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001)
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
Lahiri, S.K., Bryant, R.E. (2004). Constructing Quantified Invariants via Predicate Abstraction. In: Steffen, B., Levi, G. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2004. Lecture Notes in Computer Science, vol 2937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24622-0_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-24622-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20803-7
Online ISBN: 978-3-540-24622-0
eBook Packages: Springer Book Archive