On multiset group

On fuzzy multiset regular grammars

The main goal of this paper is to introduce and study fuzzy multiset regular grammar to show that fuzzy multiset finite automata and fuzzy multiset regular grammars are equivalent. We also study fuzzy multiset linear grammars and fuzzy multiset regular grammars in normal form. Furthermore, we show the equivalence of fuzzy multiset regular grammars, fuzzy multiset left linear grammars, fuzzy mul...

On fuzzy multiset regular languages

The purpose of present work is to study some algebraic aspect of fuzzy multiset regular languages. In between, we show the equivalence of multiset regular language and fuzzy multiset regular language. Finally, we introduce the concept of pumping lemma for fuzzy multiset regular languages, which we use to establish a necessary and sufficient condition for a fuzzy multiset language to be non-cons...

Multiset rewriting by multiset onstraint solving

On multiset colorings of graphs

A vertex coloring of a graph G is a multiset coloring if the multisets of colors of the neighbors of every two adjacent vertices are different. The minimum k for which G has a multiset k-coloring is the multiset chromatic number χm(G) of G. For every graph G, χm(G) is bounded above by its chromatic number χ(G). The multiset chromatic numbers of regular graphs are investigated. It is shown that ...

On estimating the probability multiset

Many statistical properties are determined not by the probabilities of the possible outcomes, but just by the multiset of these probabilities. We estimate this probability multiset from an observed data sample. Akin to standard maximum likelihood, which maximizes the probability of the observed outcomes, we propose profile maximum likelihood (PML), which maximizes the probability of the observe...