Results 221 to 230 of about 1,322 (256)
Order, 2012 Let \(A\) and \(B\) be sets. For functions \(f:\;A^n\to B\), \(g:\;A^m\to B\) we write \(g\leq f\) if there exists an assignment \(\alpha:\;\{1,\dots,n\}\to\{1,\dots,m\}\) such that \(g(a_1,\dots,a_m)=f(a_{\alpha(1)},\dots,a_{\alpha(n)})\) for all \(a_1,\dots,a_m\in A\).
Erkko Lehtonen +2 more
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Essential arities in algebras of finite type and arity trees
Discrete Mathematics, 2002 Given an algebra \(A\), \(S(A)\) denotes the set of those nonnegative integers \(n\) for which there is a nontrivial essentially \(n\)-ary term operation on \(A\). In 1965, K. Urbanik characterized the sets \(S\) of integers such that \(S= S(A)\) for some idempotent algebra \(A\).
Andrzej Kisielewicz
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Journal of Intelligent & Fuzzy Systems, 2021
The arity of convex spaces is a numerical feature which shows the ability of finite subsets spanning to the whole space via the hull operators. This paper gives it a formal and strict definition by introducing the truncation of convex spaces. The relations that between the arity of quotient spaces and the original spaces, that between the arity of ...
Wei Yao, Ye Chen
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The arity of convex spaces is a numerical feature which shows the ability of finite subsets spanning to the whole space via the hull operators. This paper gives it a formal and strict definition by introducing the truncation of convex spaces. The relations that between the arity of quotient spaces and the original spaces, that between the arity of ...
Wei Yao, Ye Chen
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Decompositions of functions based on arity gap [PDF]
Discrete Mathematics, 2012 We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified. We establish a complete classification of functions according to their arity gap, extending existing results for ...
Erkko Lehtonen +2 more
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A variable-arity procedural interface
Proceedings of the 1988 ACM conference on LISP and functional programming, 1988This paper presents a procedural interface that handles optional arguments and indefinite numbers of arguments in a convenient and efficient manner without resorting to storing the arguments in a language-dependent data structure. This interface solves many of the problems inherent in the use of lists to store indefinite numbers of arguments.
R. Kent Dybvig, Robert Hieb
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Computer Languages, Systems & Structures, 2014
Higher order combinators in functional programming languages can lead to code that would be considerably more efficient if some functions' definitions were eta-expanded, but the existing analyses are not always precise enough to allow that. In particular, this has prevented foldl from efficiently taking part in list fusion.
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Higher order combinators in functional programming languages can lead to code that would be considerably more efficient if some functions' definitions were eta-expanded, but the existing analyses are not always precise enough to allow that. In particular, this has prevented foldl from efficiently taking part in list fusion.
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Centralizing Monoids and the Arity of Witnesses
2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL), 2017Multi-variable functions defined over a fixed finite set A are considered. A centralizing monoid M is a set of unary functions on A which commute with all members of some set F of functions on A. The set F is called a witness of M. We show that every centralizing monoid has a witness whose arity does not exceed |A|.
Hajime Machida, Ivo G. Rosenberg
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On the real arity of multiparent recombination
Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 2003Several papers have reported experimental results for multiparent recombination operators, looking at the effects of using more parents. Tacitly, these studies assume that the number of parents (the arity of the given recombination operator) tells how many old individuals contribute to a new one by passing their genetic information to it.
Ida G. Sprinkhuizen-Kuyper +2 more
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A new approach to procedures with variable arity
Lisp and Symbolic Computation, 1990This article presents a convenient and efficient procedural interface that allows the definition and use of procedures with optional arguments and indefinite numbers of arguments without resorting to the use of a language-dependent data structure in which to store the arguments. This interface solves many of the problems inherent in the use of lists in
R. Kent Dybvig, Robert Hieb
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Concrete Dualities and Essential Arities
2014 IEEE 44th International Symposium on Multiple-Valued Logic, 2014Many dualities arise in the same way: they are induced by dualizing objects. We show that these dualities are connected to a question occurring in universal algebra. Indeed, they cause a strong interplay between the essential arity of finitary operations in one category and the concrete form of the copowers in the other. We elaborate on this connection
Sebastian Kerkhoff
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