Abstract
We introduce an efficient decision procedure for the theory of equality based on finite instantiations. When using the finite instantiations method, it is a common practice to take a range of [1..n] (where n is the number of input non-Boolean variables) as the range for all non-Boolean variables, resulting in a state-space of n n. Although various attempts to minimize this range were made, typically they either required various restrictions on the investigated formulas or were not very effective. In many cases, the n n state-space cannot be handled by BDD-based tools within a reasonable amount of time. In this paper we show that significantly smaller domains can be algorithmically found, by analyzing the structure of the formula. We also show an upper bound for the state-space based on this analysis. This method enabled us to verify formulas containing hundreds of integer and floating point variables.
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W. Ackerman. Solvable cases of the Decision Problem. Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam, 1954.
J. R. Burch and D. L. Dill. Automatic verification of pipelined microprocessor control. In Proc. CAV’94, LNCS 818, pp 68–80.
R. Bryant, S. German, and M. Velev. Exploiting positive equality in a logic of equality with uninterpreted functions. In this volume, 1999.
The Sacres Consortium. Safety critical embedded systems: from requirements to system architecture, 1995. Esprit Project Description EP 20.897, URL http://www.tni.fr/sacres.
R. Hojati, A. Isles, D. Kirkpatrick, and R.K. Brayton. Verification using uninterpreted functions and finite instantiations. FMCAD’96, pp 218–232.
R. Hojati, A. Kuehlmann, S. German, and R. Brayton. Validity checking in the theory of equality using finite instantiations. In Proc. Intl. Workshop on Logic Synthesis, 1997.
A. Pnueli, Y. Rodeh, O. Shtrichman, and M. Siegel. An efficient algorithm for the range minimization problem. Tech. report, Weizmann Institute, 1998.
A. Pnueli, M. Siegel, and O. Shtrichman. Translation validation for synchronous languages. ICALP98 LNCS 1443, pages 235–246
A. Pnueli, M. Siegel, and O. Shtrichman. The code validation tool (CVT)-automatic verification of a compilation process. Intl. journal on Software Tools for Technology Transfer (STTT), vol 2, 1999.
[SGZ+98]_ K. Sajid, A. Goel, H. Zhou, A. Aziz, S. Barber, and V. Singhal. BDD based procedures for a theory of equality with uninterpreted functions. CAV’98, LNCS 1427, pp 244–255.
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© 1999 Springer-Verlag Berlin Heidelberg
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Pnueli, A., Rodeh, Y., Shtrichman, O., Siegel, M. (1999). Deciding Equality Formulas by Small Domains Instantiations. In: Halbwachs, N., Peled, D. (eds) Computer Aided Verification. CAV 1999. Lecture Notes in Computer Science, vol 1633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48683-6_39
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DOI: https://doi.org/10.1007/3-540-48683-6_39
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