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

Bishoksan Kafle, John Patrick Gallagher, Pierre Ganty

Publikation: Bidrag til tidsskriftKonferenceartikelForskningpeer review

Resumé

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.

Konference

Konference3rd Workshop on Horn Clauses for Verification and Synthesis
LokationEindhoven
LandHolland
ByEindhoven
Periode03/04/201603/04/2016
Internetadresse

Citer dette

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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",
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language = "English",
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pages = "33--48",
journal = "Electronic Proceedings in Theoretical Computer Science",
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Solving non-linear Horn clauses using a linear Horn clause solver. / Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre.

I: Electronic Proceedings in Theoretical Computer Science, Bind 219, 2016, s. 33-48.

Publikation: Bidrag til tidsskriftKonferenceartikelForskningpeer review

TY - GEN

T1 - Solving non-linear Horn clauses using a linear Horn clause solver

AU - Kafle, Bishoksan

AU - Gallagher, John Patrick

AU - Ganty, Pierre

PY - 2016

Y1 - 2016

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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