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: This short note finds that Δ f is computed incorrectly in their paper (leading to Δ h ? 2 21 + 1 2 ) and correct their result by disproving the related conjecture for the 21-variable balanced functions.
13 citations
Posted Content•
TL;DR: The study of the local structure of idempotent finite algebras is refined, demonstrating that the edges of the graph of an algebra can be made `thin', that is, there are term operations that behave very similar to semilattice, majority, or affine operations on 2-element subsets of the algebra.
Abstract: We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an arbitrary finite idempotent algebra omitting type 1. We show that this graph is connected, its edges can be classified into 3 types corresponding to the local behavior (semilattice, majority, or affine) of certain term operations, and that the structure of the algebra can be `improved' without introducing type 1 by choosing an appropriate reduct of the original algebra. Then we refine this structure demonstrating that the edges of the graph of an algebra can be made `thin', that is, there are term operations that behave very similar to semilattice, majority, or affine operations on 2-element subsets of the algebra. Finally, we prove certain connectivity properties of the refined structures.
This research is motivated by the study of the Constraint Satisfaction Problem, although the problem itself does not really show up in this paper.
13 citations
Patent•
IBM1
TL;DR: In this article, a method for optimizing a transaction consisting of an initial sequence of computer operations, the method including identifying one or more idempotent operations in the initial sequence.
Abstract: A method for optimizing a transaction consisting of an initial sequence of computer operations, the method including identifying one or more idempotent operations in the initial sequence. The method further includes reordering the initial sequence to form a reordered sequence consisting of a first sub-sequence of the computer operations followed by a second sub-sequence of the computer operations. The second sub-sequence has only the one or more idempotent operations.
13 citations
TL;DR: In this article, it was shown that the set L (R) of all R -linear maps on M n (R ) which preserve both idempotence and nonidempotence is a proper subset of F (R), when the characteristic of R is 2.
13 citations
TL;DR: In this paper, the elements of the (maximum) idempotent generated subsemigroup of the Kauffman monoid were characterized in terms of combinatorial data associated with certain normal forms.
Abstract: We characterise the elements of the (maximum) idempotent-generated subsemigroup of the Kauffman monoid in terms of combinatorial data associated with certain normal forms. We also calculate the smallest size of a generating set and idempotent generating set.
13 citations