Computer Science – Discrete Mathematics
Scientific paper
2011-05-20
Computer Science
Discrete Mathematics
Scientific paper
The symmetric maximum, denoted by v, is an extension of the usual max operation so that 0 is the neutral element, and -x is the symmetric (or inverse) of x, i.e., x v(-x)=0. However, such an extension does not preserve the associativity of max. This fact asks for systematic ways of parenthesing (or bracketing) terms of a sequence (with more than two arguments) when using such an extended maximum. We refer to such systematic (predefined) ways of parenthesing as computation rules. As it turns out there are infinitely many computation rules each of which corresponding to a systematic way of bracketing arguments of sequences. Essentially, computation rules reduce to deleting terms of sequences based on the condition x v(-x)=0. This observation gives raise to a quasi-order on the set of such computation rules: say that rule 1 is below rule 2 if for all sequences of numbers, rule 1 deletes more terms in the sequence than rule 2. In this paper we present a study of this quasi-ordering of computation rules. In particular, we show that the induced poset of all equivalence classes of computation rules is uncountably infinite, has infinitely many maximal elements, has infinitely many atoms, and it embeds the powerset of natural numbers ordered by inclusion.
Couceiro Miguel
Grabisch Michel
No associations
LandOfFree
On the poset of computation rules for nonassociative calculus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the poset of computation rules for nonassociative calculus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the poset of computation rules for nonassociative calculus will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-712876