The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of efficient generation of interpolants for some important fragments of first-order logic, which are amenable for effective decision procedures, called satisfiability modulo theory (SMT) solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state-of-the-art algorithms for satisfiability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.

Efficient Interpolant Generation in Satisfiability Modulo Theories

Cimatti, Alessandro;Griggio, Alberto;Sebastiani, Roberto
2010-01-01

Abstract

The problem of computing Craig interpolants has recently received a lot of interest. In this article, we address the problem of efficient generation of interpolants for some important fragments of first-order logic, which are amenable for effective decision procedures, called satisfiability modulo theory (SMT) solvers. We make the following contributions. First, we provide interpolation procedures for several basic theories of interest: the theories of linear arithmetic over the rationals, difference logic over rationals and integers, and UTVPI over rationals and integers. Second, we define a novel approach to interpolate combinations of theories that applies to the delayed theory combination approach. Efficiency is ensured by the fact that the proposed interpolation algorithms extend state-of-the-art algorithms for satisfiability modulo theories. Our experimental evaluation shows that the MathSAT SMT solver can produce interpolants with minor overhead in search, and much more efficiently than other competitor solvers.
2010
1
Cimatti, Alessandro; Griggio, Alberto; Sebastiani, Roberto
File in questo prodotto:
File Dimensione Formato  
3_TOCL-INTERPOLATION-2010.pdf

Solo gestori archivio

Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.12 MB
Formato Adobe PDF
1.12 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/89117
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 51
  • ???jsp.display-item.citation.isi??? 38
social impact