2008/11/28 by Adel Bouhoula, Bouhoula, Adel, Florent Jacquemard +1
Computer Science · #Algorithms and Data Compression #Cellular Automata and Applications #Computability, Logic, AI Algorithms #F.4.1 #F.4.2 #F.4.3 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Symbolic Computation (cs.SC) #cs.LO #cs.SC
paper · pdf · doi:10.48550/arxiv.0811.4720
This is the long version of a paper which appeared in IJCAR 2008. 38 pages
arxiv created 2008/11/28 · openalex publication_date 2008/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values), and may express syntactic equality, disequality, ordering and also membership in a fixed tree language. Constrained equational axioms between constructor terms are supported and can be used in order to specify complex data structures like sets, sorted lists, trees, powerlists... Our procedure is based on tree grammars with constraints, a formalism which can describe exactly the initial model of the given specification (when it is sufficiently complete and terminating). They are used in the inductive proofs first as an induction scheme for the generation of subgoals at induction steps, second for checking validity and redundancy criteria by reduction to an emptiness problem, and third for defining and solving membership constraints. We show that the procedure is sound and refutationally complete. It generalizes former test set induction techniques and yields natural proofs for several non-trivial examples presented in the paper, these examples are difficult to specify and carry on automatically with related induction procedures.