Computer-Assisted Proving of Combinatorial Conjectures Over Finite Domains: A Case Study of a Chess Conjecture

01/23/2018
by   Predrag Janicic, et al.
0

There are several approaches for using computers in deriving mathematical proofs. For their illustration, we provide an in-depth study of using computer support for proving one complex combinatorial conjecture -- correctness of a strategy for the chess KRK endgame. The final, machine verifiable, result presented in this paper is that there is a winning strategy for white in the KRK endgame generalized to n × n board (for natural n greater than 3). We demonstrate that different approaches for computer-based theorem proving work best together and in synergy and that the technology currently available is powerful enough for providing significant help to humans deriving complex proofs.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/10/2019

Homogeneous length functions on Groups: Intertwined computer & human proofs

We describe a case of an interplay between human and computer proving wh...
research
09/04/2023

Partial Proof of a Conjecture with Implications for Spectral Majorization

In this paper we report on new results relating to a conjecture regardin...
research
05/08/2023

Computer assisted proofs for hyperbolic quasi-periodic invariant tori in dissipative twist maps

This paper outlines an approach for proving existence of hyperbolic quas...
research
03/05/2018

Prototyping "Systems that Explain Themselves" for Education

"Systems that Explain Themselves" appears a provocative wording, in part...
research
12/28/2017

Object-Oriented Theorem Proving (OOTP): First Thoughts

Automatic (i.e., computer-assisted) theorem proving (ATP) can come in ma...
research
04/27/2017

No, This is not a Circle

A popular curve shown in introductory maths textbooks, seems like a circ...
research
06/29/2019

The Ramanujan Machine: Automatically Generated Conjectures on Fundamental Constants

Fundamental mathematical constants like e and π are ubiquitous in divers...

Please sign up or login with your details

Forgot password? Click here to reset