In this paper we consider the problem of enumerating the submultisets of a multiset, in which each element has equal multiplicity. The crucial property is that consecutive submultisets in this listing differ one in the cardinality of only one of the elements. This is a generalization to k-ary numbers of the so-called Gray Codes for binary numbers. In the special case of binary numbers there is ...

athemat s.2012.1 Abstract Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset bas...

The paper gives a matrix-free presentation of the correspondence between full-length linear codes and projective multisets. It generalizes the BrouwerVan Eupen construction that transforms projective codes into two-weight codes. Short proofs of known theorems are obtained. A new notion of self-duality in coding theory is explored. 94B05, 94B27, 51E22.

I briefly discuss the facilities for programming with sets and multisets provided by the programming language Escher, which is a general-purpose, declarative language that integrates the best features of both functional and logic programming languages. Escher has types and modules, higher-order and meta-programming facilities, concurrency, and declarative input/output. The main design aim is to...

P systems are parallel molecular computing models which process multisets of objects in cell-like membrane structures. In this paper we consider the trace languages of a special symbol, the traveler, in symport/antiport P systems where, instead of multisets of objects, sets of objects were considered. Two different ways to define the trace language are proposed. One of the families of languages...

In this paper, we introduce a new paradigm multiset-based tree model. We show that trees can be represented in the form of wellfounded multisets. We also show that the conventional approach for this representation is not injective from a set of trees to the class of multisets representing such trees. We establish a oneto-one correspondence between trees and suitable permutations of a wellfounde...

The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain typ...

We define Concurrent Turing Machines (CTMs) as Turing machines with Petri nets as finite control. This leads to machines with arbitrary many tape heads, thus subsuming any class of (constant) khead Turing machines. Concurrent Turing machines correspond to a class of multiset rewriting systems. The definition of a CTMs as a rewrite theory avoids the need for encoding multisets as words and using...