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

Abstract

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.

Conference

Conference3rd Workshop on Horn Clauses for Verification and Synthesis
LocationEindhoven
CountryNetherlands
Period03/04/201603/04/2016
Internet address

Keywords

  • Program analysis
  • Program verification
  • Horn clauses

Cite this

@inproceedings{df23ea206b204aa5a3495849141a5139,
title = "Solving non-linear Horn clauses using a linear Horn clause solver",
abstract = "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.",
keywords = "Program analysis, Program verification, Horn clauses",
author = "Bishoksan Kafle and Gallagher, {John Patrick} and Pierre Ganty",
year = "2016",
doi = "10.4204/EPTCS.219.4",
language = "English",
volume = "219",
pages = "33--48",
journal = "Electronic Proceedings in Theoretical Computer Science",
issn = "2075-2180",
publisher = "Open Publishing Association",

}

Solving non-linear Horn clauses using a linear Horn clause solver. / Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre.

In: Electronic Proceedings in Theoretical Computer Science, Vol. 219, 2016, p. 33-48.

Research output: Contribution to journalConference articleResearchpeer-review

TY - GEN

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AU - Kafle, Bishoksan

AU - Gallagher, John Patrick

AU - Ganty, Pierre

PY - 2016

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N2 - 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.

AB - 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.

KW - Program analysis

KW - Program verification

KW - Horn clauses

U2 - 10.4204/EPTCS.219.4

DO - 10.4204/EPTCS.219.4

M3 - Conference article

VL - 219

SP - 33

EP - 48

JO - Electronic Proceedings in Theoretical Computer Science

JF - Electronic Proceedings in Theoretical Computer Science

SN - 2075-2180

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