On certain classes of problems, recombination is more effective if the parents that are being recombined share common subsolutions. These common subsolutions can be used to decompose the recombination space into linearly independent subproblems. If a problem can be decomposed into k subproblems, a single greedy recombination can select the best of 2 possible offspring. The idea of exploiting de...

In this article we give a partial answer to an important open problem in descriptive set theory, the Decomposability Conjecture on Borel functions from an analytic subset of a Polish space into a separable metrizable space. Our techniques employ deep results from effective descriptive set theory and recursion theory. In fact it is essential to prove that several prominent results in recursion t...

A study of assisted problem solving formalized via decompositions of deterministic finite automata is initiated. The landscape of new types of decompositions of finite automata this study uncovered is presented. Languages with various degrees of decomposability between undecomposable and perfectly decomposable are shown to exist.

Two approaches to time consistency of risk averse multistage stochastic problems were discussed in the recent literature. In one approach certain properties of the corresponding risk measure are postulated which imply its decomposability. The other approach deals directly with conditional optimality of solutions of the considered problem. The aim of this paper is to discuss a relation between t...

Some combinatorial results concerning finite decompositions (dissections) of a k-dimensional cube into cubes (respectively, simplexes) of the same dimension are presented in the paper. In connection with such decompositions, the notion of a decomposability number is introduced and the problem of description of all these numbers is discussed. 2000 Mathematics Subject Classification: 52A15, 52B05...

Motivated by the proof of Rump a conjecture Gateva-Ivanova on decomposability square-free solutions to Yang-Baxter equation, we present several other theorems based cycle structure certain permutation associated with solution.