Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
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TL;DR: In this article, the number of idempotent elements in the symmetric semigroup on n elements has been investigated and a number of combinatorial identities and congruences are given.
44 citations
TL;DR: In this paper, an evolution algebra of the bisexual population is introduced, which identifies the coefficients of inheritance of a bisexual population as the structure constants of the algebra and proves that the algebra is commutative, not associative and not necessarily power-associative.
44 citations
27 Mar 1996
TL;DR: An equational proof, using Kleene algebra with tests and commutativity conditions, of the following classical result: every while program can be simulated by a while program with at most one while loop.
Abstract: We give an equational proof, using Kleene algebra with tests and commutativity conditions, of the following classical result: every while program can be simulated by a while program with at most one while loop. The proof illustrates the use of Kleene algebra with extra conditions in program equivalence proofs. We also show, using a construction of Cohen, that the universal Horn theory of *-continuous Kleene algebras is not finitely axiomatizable.
44 citations
TL;DR: In this article, it was shown that two natural classes of semiring-semimodule pairs, the complete and the bi-inductive semiringsemimmodule pairs both give rise to iteration semiring semimodules.
Abstract: Conway semiring-module pairs and iteration semiring-semimodule pairs were shown to provide an axiomatic basis to automata on ω -words in [Bloom, Esik: Iteration Theories, Springer, 1993]. In this paper, we show that two natural classes of semiring-semimodule pairs, the complete and the bi-inductive semiring-semimodule pairs both give rise to iteration semiring-semimodule pairs. Complete semiring-semimodule pairs are defined by infinite sums and products, while a bi-inductive semiring-semimodule pair is an ordered semiring-semimodule pair possessing enough least pre-fixed points and greatest post-fixed points to solve linear inequations. Moreover, we show that when V is idempotent, then a semiring-semimodule pair equipped with a star and an omega operation satisfies the Conway equations (iteration semiring-semimodule pair equations, respectively) if and only if the quemiring associated with (S,V) embeds in a Conway semiring (iteration semiring, respectively).
44 citations
TL;DR: In this article, the authors studied the structure of the partial Brauer monoid and its planar sub-monoid, the Motzkin monoid, and obtained necessary and sufficient conditions under which the ideals of these monoids are idempotent-generated.
43 citations