Arithmetic constraints in solving helpmate problems

Chess can be considered as a complex system of arithmetic constraints. There exist both geometric constraints (relationships of pieces on the board) and time constraints (number and order of moves within several variations) in chess. This paper describes a new search stragegy that uses arithmetic constraints to solve a special class of chess problems, so-called helpmates with a very small number of pieces. The algorithm introduced here was developed using a Constraint Logic Programming language CLP(R) and tested in helpmates of the type "king and piece against king and piece". The algorithm is to be ported now to the smarter Oz programming system.