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Nelson-Oppen, Shostak and the Extended Canonizer: A Family Picture with a Newborn

Silvio Ranise 1 Christophe Ringeissen 2 Duc-Khanh Tran 2 
1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
2 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We consider the problem of building satisfiability procedures for unions of disjoint theories. We briefly review the combination schemas proposed by Nelson-Oppen, Shostak, and others. Three inference systems are directly derived from the properties satisfied by the theories being combined and known results from the literature are obtained in a uniform and abstract way. This rational reconstruction is the starting point for further investigations. We introduce the concept of extended canonizer and derive a modularity result for a new class of theories (larger than Shostak and smaller than Nelson-Oppen theories) which is closed under disjoint union. This is in contrast with the lack of modularity of Shostak theories. We also explain how to implement extended canonizers by using the basic building blocks used in Shostak schema or by means of rewriting techniques.
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Submitted on : Tuesday, September 26, 2006 - 10:13:05 AM
Last modification on : Friday, January 21, 2022 - 3:09:06 AM


  • HAL Id : inria-00099985, version 1


Silvio Ranise, Christophe Ringeissen, Duc-Khanh Tran. Nelson-Oppen, Shostak and the Extended Canonizer: A Family Picture with a Newborn. First International Colloquium on Theoretical Aspects of Computing - ICTAC 2004, Keijiro Araki, Zhiming Liu, 2004, Guiyang, Chine, 15 p. ⟨inria-00099985⟩



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