# Automata-driven automated induction

@article{Bouhoula1997AutomatadrivenAI, title={Automata-driven automated induction}, author={Adel Bouhoula and Jean-Pierre Jouannaud}, journal={Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science}, year={1997}, pages={14-25} }

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…

## 7 Citations

Automated Induction for Complex Data Structures

- Computer ScienceArXiv
- 2008

A procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints 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).

Sufficient Completeness Verification for Conditional and Constrained Term Rewriting Systems

- Computer Science
- 2017

A procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained, which allows to specify complex data structures like e.g. sets, sorted lists or powerlists.

A Simple Deduction System for First-Order Logic with Equality, Free Constructors and Induction

- Computer Science
- 1999

This work proposes a sequent system for a logic where terms can be built only from variables and free constructors, and extends the system to include first-order structural induction principles on datatype values.

Sufficient completeness verification for conditional and constrained TRS

- Computer ScienceJ. Appl. Log.
- 2012

Superposition for fixed domains

- PhilosophyTOCL
- 2010

The first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain is proposed, which is sound and refutationally complete in the limit for a first-order fixed domain semantics.

Automating Sufficient Completeness Check for Conditional and Constrained TRS

- Computer Science
- 2006

A procedure for checking sufficient completeness for conditional and constrained term rewriting systems containing axioms for constructors which may be constrained, which allows to specify complex data structures like e.g. sets, sorted lists or powerlists.

Austrian-Japanese Workshop on Symbolic Computation in Software Science

- Computer Science
- 2008

A refined system of rewriting induction is presented with an increased capability of non-orientable theorems and a capability of disproving incorrect conjectures.

Mechanically certifying formula-based Noetherian induction reasoning

- Computer ScienceJ. Symb. Comput.
- 2017

Alternating Two − Way AC − Tree Automata Research Report LSV

- Computer Science
- 2002

It is shown that the use of conditional push clauses, or of alternation, leads to undecidability, already in the case of one AC or AC1 symbol, with only functions of arity zero, while emptiness is decidable in the general case of many function symbols, including many AC orAC1 symbols, provided push clauses are unconditional and intersection clauses are final.