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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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Journal ArticleDOI
TL;DR: The call-by-value CPS transformation is rephrase to make it syntactically idempotent, modulo eta-reduction of the newly introduced continuation.
Abstract: The CPS (continuation-passing style) transformation on typed lambda-terms has an interpretation in many areas of Computer Science, such as programming languages and type theory. Programming intuition suggests that in effect, it is idempotent, but this does not directly hold for all existing CPS transformations (Plotkin, Reynolds, Fischer, etc.). We rephrase the call-by-value CPS transformation to make it syntactically idempotent, modulo eta-reduction of the newly introduced continuation. Type-wise, iterating the transformation corresponds to refining the polymorphic domain of answers.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors construct the first example of a just non-finitely based variety of big groups, i.e., a variety which is not necessarily finitely based but all the proper subvarieties are finitely-based.
Abstract: A bigroup is a pair (H, π) consisting of a group H and an idempotent endomorphism π of H. One can consider π as a unary operation on H so a bigroup is a universal algebra. The aim of our paper is to construct the first example of a just non-finitely based variety of bigroups i.e. a variety which is non-finitely based but all whose proper subvarieties are finitely based. There is a close similarity between varieties of bigroups and varieties of groups so we hope that our result could help to construct a just non-finitely based variety of groups. *The first author was supported by NSERC, Canada.

6 citations

Journal ArticleDOI
TL;DR: In this paper, a finite-dimensional unital commutative algebra carrying an associative positive definite bilinear form is defined, and there exists a nonzero idempotent c ∆ ≥ 0 (e be...
Abstract: If V is a finite-dimensional unital commutative (maybe nonassociative) algebra carrying an associative positive definite bilinear form 〈, 〉 then there exist a nonzero idempotent c ≠ e (e be...

6 citations

Posted Content
TL;DR: It is shown how to approximate cambG,X by means of rational formal power series, and a lower bound on the convergence speed of these approximations is given, which extends Parikh’s well-known result that the commutative image of context-free languages is semilinear.
Abstract: The commutative ambiguity cambG,X of a context-free grammar G with start symbol X assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton’s method to !-continuous semirings [EKL07b, EKL07a, EKL10], we show how to approximate cambG,X by means of rational formal power series, and give a lower bound on the convergence speed of these approximations. From the latter result we deduce that cambG,X itself is rational modulo the generalized idempotence identity k = k + 1 (for k some positive integer), and, subsequently, that it can be represented as a weighted sum of linear sets. This extends Parikh’s well-known result that the commutative image of context-free languages is semilinear (k = 1). Based on the well-known relationship between context-free grammars and algebraic systems over semirings [CS63, SS78, BR82, Kui97, Boz99], our results extend the work by Green et al. [GKT07] on the computation of the provenance of Datalog queries over commutative !-continuous semirings.

6 citations

Journal ArticleDOI
Ines Klimann1
TL;DR: A standard problem of control theory, the (A; B)-invariance problem, which amounts to computing a maximal element X subject to conditions of the form AX 6 X + B and X 6 K, is studied.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023106
2022263
202184
2020100
201991
201892