Solving finite-domain linear constraints in presence of the alldifferent\texttt{alldifferent}

In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that the variables in a linear constraint are also constrained by some alldifferent constraints may help us to calculate stronger bounds of the variables, leading to a stronger constraint propagation. We propose an improved filtering algorithm that targets such cases. We provide a detailed description of the proposed algorithm and prove its correctness. We evaluate the approach on five different problems that involve combinations of the linear and the alldifferent constraints. We also compare our algorithm to other relevant approaches. The experimental results show a great potential of the proposed improvement.Comment: 28 pages, 2 figure

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

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 $n \times n$ 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

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

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 $n \times n$ 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