Rewriting induction + linear arithmetic = decision procedure

Authors:
Stephan Falke;Deepak Kapur
Affiliations:
Inst. for Theoretical Computer Science, KIT, Germany;Dept. of Computer Science, University of New Mexico
Venue:
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Year:
2012

Citing 14
Cited 0

Integrating decision procedures into heuristic theorem provers: a case study of linear arithmetic

Machine intelligence 11
Automating inductionless induction using test sets

Journal of Symbolic Computation
Automated theorem proving by test set induction

Journal of Symbolic Computation
Term rewriting and all that

Term rewriting and all that
Incorporating decision procedures in implicit induction

Journal of Symbolic Computation - Integrated reasoning and algebra systems
Term Rewriting Induction

Proceedings of the 10th International Conference on Automated Deduction
Extending Decision Procedures with Induction Schemes

CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Decidable Classes of Inductive Theorems

IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Automated Induction with Constrained Tree Automata

IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Inductive proof search modulo

Annals of Mathematics and Artificial Intelligence
CVC3

CAV'07 Proceedings of the 19th international conference on Computer aided verification
Inductive decidability using implicit induction

LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A fast linear-arithmetic solver for DPLL(T)

CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Dealing with non-orientable equations in rewriting induction

RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents new results on the decidability of inductive validity of conjectures. For these results, a class of term rewrite systems (TRSs) with built-in linear integer arithmetic is introduced and it is shown how these TRSs can be used in the context of inductive theorem proving. The proof method developed for inductive theorem proving couples (implicit) inductive reasoning with a decision procedure for the theory of linear integer arithmetic with (free) constructors. The effectiveness of the new decidability results on a large class of conjectures is demonstrated by an evaluation of the prototype implementation Sail2.