The Automation of Proof by Mathematical Induction

The Automation of Proof by Mathematical Induction 31

The Dynamic Creation of Induction Rules Using Proof Planning

A key problem in automating proof by mathematical induction is choosing an induction rule suitable for a given conjecture. Since Boyer & Moore’s NQTHM system the standard approach has been based on recursion analysis, which uses a combination of induction rules based on the relevant recursive function definitions. However, there are practical examples on which such techniques are known to fail....

Integrating Implicit Induction Proofs into Certified Proof Environments

We give evidence of the direct integration and automated checking of implicit induction-based proofs inside certified reasoning environments, as that provided by the Coq proof assistant. This is the first step of a long term project focused on 1) mechanically certifying implicit induction proofs generated by automated provers like Spike, and 2) narrowing the gap between automated and interactiv...

Proof Planning and Program Synthesis: A Survey

Proof planning is a knowledge-based automated theorem proving t~hnlque. It has been applied to a number of theorem-proving domains, for example: mathematical induction (Bundy et al.1991), and hardware verification (Cantu et a/.1996) (to pick two of the many). In the domain of program synthesis, it has been used to automate the synthesis of logic (Kraan et a/.1993a, Kraan et al.1993b, Basin et a...

On the Closed-Form Solution of a Nonlinear Difference Equation and Another Proof to Sroysang’s Conjecture

The purpose of this paper is twofold. First we derive theoretically, using appropriate transformation on x(n), the closed-form solution of the nonlinear difference equation x(n+1) = 1/(±1 + x(n)), n ∈ N_0. The form of solution of this equation, however, was first obtained in [10] but through induction principle. Then, with the solution of the above equation at hand, we prove a case ...