A Chess Composer of Two-Move Mate Problems

A Deep Improver of Two-move Chess Mate Problems

Evolution of an Efficient Search Algorithm for the Mate-In-N Problem in Chess

We propose an approach for developing efficient search algorithms through genetic programming. Focusing on the game of chess we evolve entire game-tree search algorithms to solve the Mate-In-N problem: find a key move such that even with the best possible counterplays, the opponent cannot avoid being mated in (or before) move N . We show that our evolved search algorithms successfully solve sev...

How Relevant Are Chess Composition Conventions?

Composition conventions are guidelines used by human composers in composing chess problems. They are particularly significant in composition tournaments. Examples include, not having any ‘check’ in the first move of the solution and not ‘dressing up’ the board with unnecessary pieces. Conventions are often associated or even directly conflated with the overall aesthetics or beauty of a composit...

New Directions in Enumerative Chess Problems

Normally a chess problem must have a unique solution, and is deemed unsound even if there are alternatives that differ only in the order in which the same moves are played. In an enumerative chess problem, the set of moves in the solution is (usually) unique but the order is not, and the task is to count the feasible permutations via an isomorphic problem in enumerative combinatorics. Almost al...

The Mate-in-n Problem of Infinite Chess Is Decidable

The mate-in-n problem of infinite chess—chess played on an infinite edgeless board—is the problem of determining whether a designated player can force a win from a given finite position in at most n moves. Although a straightforward formulation of this problem leads to assertions of high arithmetic complexity, with 2n alternating quantifiers, the main theorem of this article nevertheless confir...