On the Notion of a Generalized Mapping on Multiset Spaces

TL;DR

This paper introduces a generalized framework for multiset mappings, unifying and extending previous models to better understand multiset processing and rewriting transformations across various contexts.

Contribution

It proposes a new generalized notion of multiset mapping that encompasses many existing models and addresses longstanding challenges in multiset transformation studies.

Findings

Unified framework for multiset mappings

Models diverse multiset rewriting transformations

Extends prior theories of Parikh, Hickman, Khomenko, and Nazmul

Abstract

This work presents a generalized notion of multiset mapping thus resolving a long standing obstacle in structural study of multiset processing. It has been shown that the mapping defined herein can model a vast array of notions as special cases and also handels diverse situations in multiset rewriting transformations. Specifically, this paper unifies and generalizes the works of Parikh(1966), Hickman(1980), Khomenko(2003) and Nazmul(2013).