Automatic Decidability for Theories Modulo Integer Offsets - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2012

Automatic Decidability for Theories Modulo Integer Offsets


Many verification problems can be reduced to a satisfiability problem modulo theories. For building satisfiability procedures the rewriting-based approach uses a general calculus for equational reasoning named superposition. Schematic superposition, in turn, provides a mean to reason on the derivations computed by superposition. Until now, schematic superposition was only studied for standard superposition. We present a schematic superposition calculus modulo a fragment of arithmetics, namely the theory of Integer Offsets. This new schematic calculus is used to prove the decidability of the satisfiability problem for some theories extending Integer Offsets. We illustrate our theoretical contribution on theories representing extensions of classical data structures, e.g., lists and records. An implementation in the rewriting-based Maude system constitutes a practical contribution. It enables automatic decidability proofs for theories of practical use.
Fichier principal
Vignette du fichier
8139.pdf (546.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00753896 , version 1 (19-11-2012)


  • HAL Id : hal-00753896 , version 1


Elena Tushkanova, Christophe Ringeissen, Alain Giorgetti, Olga Kouchnarenko. Automatic Decidability for Theories Modulo Integer Offsets. [Research Report] RR-8139, INRIA. 2012, pp.20. ⟨hal-00753896⟩
214 View
99 Download


Gmail Facebook X LinkedIn More