Parsing Partially Ordered Multisets

A partially ordered multiset or pomset is a generalization of a string in which the total order has been relaxed to a partial order. Strings are often used as a model for sequential computation; pomsets are a natural model for parallel and distributed computation. By viewing pomsets as a generalization of strings, the question is raised whether concepts from language theory can be generalized to pomsets. An important area in the theory of languages is parsing theory. This paper develops the fundamentals of a parsing theory for pomsets, called PLR parsing. It is based on the LR-parsing technique, which is the most powerful deterministic parsing technique in language theory. The basic algorithm in the class of PLR parsing algorithms, the PLR(0) algorithm is explained in detail. Keywords: partial orders -- partially ordered multisets -- pomset languages -- pomset grammars -- LR parsing -- PLR parsing -- concurrency theory 1. Introduction Gischer introduces partially ordered multisets o..