Tree dimension in verification of constrained Horn clauses. Issue 2 (11th May 2018)

• Record Type: Journal Article
• Authors: KAFLE, BISHOKSAN; GALLAGHER, JOHN P.; GANTY, PIERRE
• Is Part Of: Theory and practice of logic programming. Volume 18:Issue 2(2018)
• Page Start: 224
• Page End: 251
• Publication Date: 2018-05-11
• Subjects: Specification, -- analysis and verification of systems, -- Horn clauses, -- tree dimension; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068418000030
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: In 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 CHCs P, we define a transformation of P yielding a dimension-bounded set of CHCs P ≤ k . The set of derivations for P ≤ k consists of the derivations for P that have dimension at most k . We also show how to construct a set of clauses denoted P > k whose derivations have dimension exceeding k . 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.