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Tree dimension in verification of constrained Horn clauses

Published online by Cambridge University Press:  11 May 2018

BISHOKSAN KAFLE ,
JOHN P. GALLAGHER Open the ORCID record for JOHN P. GALLAGHER [Opens in a new window]  and
PIERRE GANTY
BISHOKSAN KAFLE
Affiliation:
School of Computing and Information Systems, The University of Melbourne, Melbourne, Victoria, Australia (e-mail: bishoksank@unimelb.edu.au)
JOHN P. GALLAGHER
Affiliation:
Department of People and Technology, Roskilde University, Roskilde, Denmark, and IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain, IMDEA Software Institute (e-mail: jpg@ruc.dk)
PIERRE GANTY
Affiliation:
IMDEA Software Institute, Pozuelo de Alarcón, Madrid, Spain (e-mail: pierre.ganty@imdea.org)
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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.

Keywords

Specificationanalysis and verification of systemsHorn clausestree dimension
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 18 , Special Issue 2: Computational Logic for Verification , March 2018 , pp. 224 - 251
Copyright
Copyright © Cambridge University Press 2018 

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