Invariant synthesis for combined theories

D. Beyer, T.A. Henzinger, R. Majumdar, A. Rybalchenko, in:, Springer, 2007, pp. 378–394.

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Abstract
We present a constraint-based algorithm for the synthesis of invariants expressed in the combined theory of linear arithmetic and uninterpreted function symbols. Given a set of programmer-specified invariant templates, our algorithm reduces the invariant synthesis problem to a sequence of arithmetic constraint satisfaction queries. Since the combination of linear arithmetic and uninterpreted functions is a widely applied predicate domain for program verification, our algorithm provides a powerful tool to statically and automatically reason about program correctness. The algorithm can also be used for the synthesis of invariants over arrays and set data structures, because satisfiability questions for the theories of sets and arrays can be reduced to the theory of linear arithmetic with uninterpreted functions. We have implemented our algorithm and used it to find invariants for a low-level memory allocator written in C.
Publishing Year
Date Published
2007-01-01
Acknowledgement
This research was sponsored in part by the grants NSF-CCF-0427202 and NSF-CCF-0546170.
Volume
4349
Page
378 - 394
Conference
VMCAI: Verification, Model Checking and Abstract Interpretation
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Beyer D, Henzinger TA, Majumdar R, Rybalchenko A. Invariant synthesis for combined theories. In: Vol 4349. Springer; 2007:378-394. doi:10.1007/978-3-540-69738-1_27
Beyer, D., Henzinger, T. A., Majumdar, R., & Rybalchenko, A. (2007). Invariant synthesis for combined theories (Vol. 4349, pp. 378–394). Presented at the VMCAI: Verification, Model Checking and Abstract Interpretation, Springer. https://doi.org/10.1007/978-3-540-69738-1_27
Beyer, Dirk, Thomas A Henzinger, Ritankar Majumdar, and Andrey Rybalchenko. “Invariant Synthesis for Combined Theories,” 4349:378–94. Springer, 2007. https://doi.org/10.1007/978-3-540-69738-1_27.
D. Beyer, T. A. Henzinger, R. Majumdar, and A. Rybalchenko, “Invariant synthesis for combined theories,” presented at the VMCAI: Verification, Model Checking and Abstract Interpretation, 2007, vol. 4349, pp. 378–394.
Beyer D, Henzinger TA, Majumdar R, Rybalchenko A. 2007. Invariant synthesis for combined theories. VMCAI: Verification, Model Checking and Abstract Interpretation, LNCS, vol. 4349. 378–394.
Beyer, Dirk, et al. Invariant Synthesis for Combined Theories. Vol. 4349, Springer, 2007, pp. 378–94, doi:10.1007/978-3-540-69738-1_27.

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