Solving non-linear Horn clauses using a linear Horn clause solver

Bishoksan Kafle, John Patrick Gallagher, Pierre Ganty

Research output: Contribution to journalConference articleResearchpeer-review


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.
Original languageEnglish
JournalElectronic Proceedings in Theoretical Computer Science
Pages (from-to)33-48
Publication statusPublished - 2016
Event3rd Workshop on Horn Clauses for Verification and Synthesis: Workshop affiliated with ETAPS 2016 (The European Joint Conferences on Theory and Practice of Software) - Eindhoven, Eindhoven, Netherlands
Duration: 3 Apr 20163 Apr 2016


Conference3rd Workshop on Horn Clauses for Verification and Synthesis
Internet address


  • Program analysis
  • Program verification
  • Horn clauses

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