6,084 research outputs found
Davenport constant for semigroups II
Let be a finite commutative semigroup. The Davenport constant
of , denoted , is defined to be the least
positive integer such that every sequence of elements in
of length at least contains a proper subsequence
() with the sum of all terms from equaling the sum of all terms
from . Let be a prime power, and let \F_q[x] be the ring of
polynomials over the finite field \F_q. Let be a quotient ring of
\F_q[x] with 0\neq R\neq \F_q[x]. We prove that where denotes
the multiplicative semigroup of the ring , and denotes
the group of units in .Comment: In press in Journal of Number Theory. arXiv admin note: text overlap
with arXiv:1409.1313 by other author
A Fuzzy Petri Nets Model for Computing With Words
Motivated by Zadeh's paradigm of computing with words rather than numbers,
several formal models of computing with words have recently been proposed.
These models are based on automata and thus are not well-suited for concurrent
computing. In this paper, we incorporate the well-known model of concurrent
computing, Petri nets, together with fuzzy set theory and thereby establish a
concurrency model of computing with words--fuzzy Petri nets for computing with
words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of
transitions are some special words modeled by fuzzy sets. By employing the
methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which
makes it possible for computing with more words. The language expressiveness of
the two formal models of computing with words, fuzzy automata for computing
with words and FPNCWs, is compared as well. A few small examples are provided
to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure
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