Results 11 to 20 of about 2,753 (280)
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 \(a_1,\dots,a_m\in A\).
MIGUEL Couceiro +2 more
exaly +7 more sources
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 ...
MIGUEL Couceiro +2 more
exaly +7 more sources
The Arity Hierarchy in the Polyadic μ-Calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 The polyadic mu-calculus is a modal fixpoint logic whose formulas define relations of nodes rather than just sets in labelled transition systems. It can express exactly the polynomial-time computable and bisimulation-invariant queries on finite graphs.
Martin Lange
core +5 more sources
A Survey on the Arity Gap [PDF]
2011 41st IEEE International Symposium on Multiple-Valued Logic, 2011 The arity gap of a function of several variables is defined as the minimum decrease in the number of essential variables when essential variables of the function are identified. We present a brief survey on the research done on the arity gap, from the first studies of this notion up to recent developments, and discuss some natural extensions and ...
Miguel Couceiro +2 more
openaire +5 more sources
Geometric convergence rates for cardinal spline subdivision with general integer arity
Journal of Numerical Analysis and Approximation Theory, 2019 A rigorous convergence analysis is presented for arbitrary order cardinal spline subdivision with general integer arity, for which the binary case, with arity two, is a well-studied subject.
Johan de Villiers +1 more
core +10 more sources
Arity-generic datatype-generic programming [PDF]
Proceedings of the 4th ACM SIGPLAN workshop on Programming languages meets program verification, 2010 Some programs are doubly-generic. For example, map is datatype-generic in that many different data structures support a mapping operation. A generic programming language like Generic Haskell can use a single definition to generate map for each type. However, map is also arity-generic because it belongs to a family of related operations that differ in ...
Stephanie Weirich, Chris Casinghino
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Applied Categorical Structures, 2021 We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends (resp., coends) of higher arity, dubbed herein $(p,q)$-ends (resp., $(p,q)$-coends). While higher arity co/ends are
Fosco Loregiàn +1 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
exaly +3 more sources
Characteristic Sequence of Strongly Minimal Directed Single Graphs of 1-Arity
Computation, 2022 In this paper, we will classify the strongly minimal directed single graphs of 1-arity by axiomatizing the theory of characteristic sequence of such a graph. Then we will show this theory is complete by using Łos-Vaught test. Complete theory is important
Abeer M. Albalahi
core +2 more sources
Reducing the arity in unbiased black-box complexity [PDF]
Theoretical Computer Science, 2012 An extended abstract of this paper has been accepted for inclusion in the proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2012)
Doerr, Benjamin, Doerr, Carola
core +8 more sources