We prove that, given a nite set of words S, there exists at most one (normalized) multiset P such that S is the shuue of the words in P. The multiset P is eeectively computable.

Abstract Fuzzy multiset finite automata with output represent fuzzy version of (with output) working over multisets. This paper introduces Mealy-like, Moore-like, and compact automata. Their mutual transformations are described to prove their equivalent behaviours. Furthermore, various variants reduced studied where the reductions directed decrease number components (like initial distribution, ...

general, any n-sequence determines a multiset of (= n!/k!(n-k)!) k-sequences. "J Suppose, conversely, that we are given a multiset 01 k-sequences. Does that multiset come from some sequence? If so, is the source sequence unique? Such questions are reminiscent of the problem of reconstructing graphs from vertex-deleted sub raphs, which has received a great deal of attention in the last twent yea...

The privacy preserving multiset union (PPMU) protocol allows a set of parties, each with a multiset, to collaboratively compute a multiset union secretly, meaning that any information other than union is not revealed. We propose an efficient PPMU protocol, using multiplicative homomorphic property of ElGamal encryption over Fq[x]/f(x) where q is a prime and f(x) is an irreducible polynomial ove...

We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of n elements supporting access in time O(1) and insertion and deletion in time O(n ) for > 0 while using o(n) extra space. We consider several different implementation optimizations in C++ and compare their performance to that of vector and multiset from the standard library on sequences...

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 ...

In this paper, we survey on reaction automata theory to model and analyze the biochemical behaviors of vital reactions occurring in nature. Inspired by two notions a system initiated Ehrenfeucht Rozenberg 2007 multiset, (RAs) have been proposed as computing models for accepting string languages. Given an input sequence symbols, RA performs its computation process follows: at every time receivin...

In this paper, we study the Stanley depth for the partially ordered set (poset) of nonempty submultisets of a multiset. We find the Stanley depth explicitly for any multiset with at most five distinct elements and provide an upper bound for the general case. On the other hand, the elements of a product of chains corresponds to the submultisets of a multiset. We prove that the Stanley depth of t...

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 number is determined for every complete multipartite graph as...