Abstract
AbstractIn this paper, we show how the notion of tree dimension can be used in the verification of constrained Horn clauses (CHCs). The dimension of a tree is a numerical measure of its branching complexity and the concept here applies to Horn clause derivation trees. Derivation trees of dimension zero correspond to derivations using linear CHCs, while trees of higher dimension arise from derivations using non-linear CHCs. We show how to instrument CHCs predicates with an extra argument for the dimension, allowing a CHC verifier to reason about bounds on the dimension of derivations. Given a set of CHCsP, we define a transformation ofPyielding adimension-boundedset of CHCsP≤k. The set of derivations forP≤kconsists of the derivations forPthat have dimension at mostk. We also show how to construct a set of clauses denotedP>kwhose derivations have dimension exceedingk. We then present algorithms using these constructions to decompose a CHC verification problem. One variation of this decomposition considers derivations of successively increasing dimension. The paper includes descriptions of implementations and experimental results.
Publisher
Cambridge University Press (CUP)
Subject
Artificial Intelligence,Computational Theory and Mathematics,Hardware and Architecture,Theoretical Computer Science,Software
Reference36 articles.
1. Computer Aided Verification
2. Peralta J. , Gallagher J. P. and Sağlam H. 1998. Analysis of imperative programs through analysis of constraint logic programs. In Proc. of International Static Analysis Symposium (SAS), G. Levi , Ed. Lecture Notes in Computer Science, vol. 1503. Springer-Verlag, 246–261.
3. Mordvinov D. and Fedyukovich G. 2017. Synchronizing constrained horn clauses. In Proc. of 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR-21), T. Eiter and D. Sands , Eds. EPiC Series in Computing, vol. 46. EasyChair, 338–355.
4. Rümmer P. , Hojjat H. and Kuncak V. 2013. Disjunctive interpolants for Horn-clause verification. In Proc. of Computer-Aided Verification, N. Sharygina and H. Veith , Eds. Lecture Notes in Computer Science, vol 8044. Springer, 347–363.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献