GAP vs. PAG

We propose a parametrized version of arity gap. The parametrized arity gap gap(f, ℓ) of a function f: A n → B measures the minimum decrease in the number of essential variables of f when ℓ consecutive identifications of pairs of essential variables are performed. We determine gap(f, ℓ) for an arbitr...

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Bibliographic Details
Published in2012 IEEE 42nd International Symposium on Multiple-Valued Logic pp. 268 - 273
Main Authors Couceiro, M., Lehtonen, E., Waldhauser, T.
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2012
Subjects
Cognition
Educational institutions
Electronic mail
Polynomials
Upper bound
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Summary:We propose a parametrized version of arity gap. The parametrized arity gap gap(f, ℓ) of a function f: A n → B measures the minimum decrease in the number of essential variables of f when ℓ consecutive identifications of pairs of essential variables are performed. We determine gap(f, ℓ) for an arbitrary function f and a positive integer ℓ. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions.
ISBN:9781467309080
1467309087
ISSN:0195-623X
2378-2226
DOI:10.1109/ISMVL.2012.11