Automated Induction with Constrained Tree Automata
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Simultaneous checking of completeness and ground confluence for algebraic specifications
ACM Transactions on Computational Logic (TOCL)
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
"Term partition" for mathematical induction
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
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Semantics and algebraic specification
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This work investigates inductive theorem proving techniques for first-order functions whose meaning and domains can be specified by Horn clauses built up from the equality and finitely many unary membership predicates. In contrast with other works in the area, constructors are not assumed to be free. Techniques originating from tree automata are used to describe ground constructor terms in normal form, on which the induction proofs are built up. Validity of (free) constructor clauses is checked by an original technique relying on the recent discovery of a complete axiomatization of finite trees and their rational subsets. Validity of clauses with defined symbols or nonfree constructor terms is reduced to the latter case by appropriate inference rules using a notion of ground reducibility for these symbols. We show how to check this property by generating proof obligations which can be passed over to the inductive prover.