Results 1 to 10 of about 326,712 (227)
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 +6 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 +6 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
exaly +5 more sources
The Arity Gap of Polynomial Functions over Bounded Distributive Lattices [PDF]
2010 40th IEEE International Symposium on Multiple-Valued Logic, 2010 Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to B is the minimum decrease in its essential arity when essential arguments of f are identified. In this paper we study the arity gap of polynomial functions over bounded distributive lattices and present a complete classification of such functions in terms ...
MIGUEL Couceiro, Erkko Lehtonen
exaly +4 more sources
The arity gap of order-preserving functions and extensions of pseudo-Boolean functions [PDF]
Discrete Applied Mathematics, 2012 The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are so-called aggregation functions. We first explicitly classify the Lovász extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between
MIGUEL Couceiro +2 more
exaly +5 more sources
Generalizations of Świerczkowski’s lemma and the arity gap of finite functions
Discrete Mathematics, 2009 Swierczkowski's Lemma - as it is usually formulated - asserts that if f is an at least quaternary operation on a finite set A and every operation obtained from f by identifying a pair of variables is a projection, then f is a semiprojection. We generalize this lemma in various ways. First, it is extended to B-valued functions on A instead of operations
MIGUEL Couceiro, Erkko Lehtonen
exaly +6 more sources
Minor complexity of discrete functions [PDF]
Applied Computing and Informatics, 2021 In this paper we study a class of complexity measures, induced by a new data structure for representing k-valued functions (operations), called minor decision diagram.
Slavcho Shtrakov
doaj +1 more source
On finite functions with non-trivial arity gap [PDF]
Discussiones Mathematicae - General Algebra and Applications, 2010 Jörg Koppitz, Slavcho Shtrakov
exaly +2 more sources
Assessing Corpus Evidence for Formal and Psycholinguistic Constraints on Nonprojectivity
Computational Linguistics, 2022 Formal constraints on crossing dependencies have played a large role in research on the formal complexity of natural language grammars and parsing. Here we ask whether the apparent evidence for constraints on crossing dependencies in treebanks might ...
Himanshu Yadav +2 more
doaj +1 more source
Finite Symmetric Functions with Non-Trivial Arity Gap
Serdica Journal of Computing, 2013 Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)).
Shtrakov, Slavcho, Koppitz, Jörg
openaire +4 more sources