2016/07/15 by Bishoksan Kafle, John P. Gallagher, Pierre Ganty
Computer Science · #cs.PL #cs.LO
paper · pdf · doi:10.4204/eptcs.219.4
published as EPTCS 219, 2016, pp. 33-48 · In Proceedings HCVS2016, arXiv:1607.04033
arxiv created 2016/07/15 · arxiv updated 2016/07/18
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm then proceeds by applying the linearisation transformation and solver for linear Horn clauses to a sequence of sets of clauses with successively increasing dimension bound. The approach is then further developed by using a solution of clauses of lower dimension to (partially) linearise clauses of higher dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise.