Multiset Processing Mathematical, Computer Science, and Molecular Computing Points of View

The multiset, as a set with multiplicities associated with its elements in the form of natural numbers, is a notation which has appeared again and again in various areas of mathematics and computer science. As a data structure, multisets stand in-between strings/lists, where a linear ordering of symbols/items is present, and sets, where no ordering and no multiplicity is considered. This book presents a selection of thoroughly reviewed revised full papers contributed to a workshop on multisets held in Curtea de Arges, Romania in August 2000 together with especially commissioned papers. All in all, the book assesses the state of the art of the notion of multisets, the mathematical background, and the computer science and molecular computing relevance.

Structures and Bio-language to Simulate Transition P Systems on Digital Computers.- Gamma and the Chemical Reaction Model: Fifteen Years After.- Visual Multiset Rewriting: Applications to Diagram Parsing and Reasoning.- Multiset Automata.- Parikh Mapping and Iteration.- Multiset Constraints and P Systems.- Toward a Formal Macroset Theory.- Normal Forms of Grammars, Finite Automata, Abstract Families, and Closure Properties of Multiset Languages.- On Multisets in Database Systems.- Tolerance Multisets.- Fuzzy Multisets and Their Generalizations.- Universality Results for Some Variants of P Systems.- Multiset and K-Subset Transforming Systems.- On P Systems with Active Membranes Solving the Integer Factorization Problem in a Polynomial Time.- The Linear Theory of Multiset Based Dynamic Systems.- Artificial Life Applications of a Class of P Systems: Abstract Rewriting Systems on Multisets.- Mathematics of Multisets.