Hierarchies of parallel rewriting P systems — A survey

The paper is about some families of rewriting P systems, where the application of evolution rules is extended from the classical sequential rewriting to the parallel one (as, for instance, in Lindenmayer systems). As a result, consistency problems for the communication of strings may arise. Three variants of parallel rewriting P systems (already present in the literature) are considered here, together with the strategies they use to face the communication problem, and some parallelism methods for string rewriting are defined. We give a survey of all known results about each variant and we state some relations among the three variants, thus establishing hierarchies of parallel rewriting P systems. Various open problems related to the subject are also presented. Danicla Besozzi: She is assistant professor at the University of Milano. She received her M.S. in Mathematics (2000) from the University of Como and Ph.D. in Computer Science (2004) from the University of Milano. Her research interests cover topics in Formal Language Theory, Molecular Computing, Systems Biology. She is member of EATCS (European Association for Theoretical Computer Science) and EMCC (European Molecular Computing Consortium). Giancarlo Mauri: He is full professor of Computer Science at the University of Milano-Bicocca. His research interests are mainly in the area of theoretical computer science, and include: formal languages and automata, computational complexity, computational learning theory, soft computing techniques, cellular automata, bioinformatics and molecular computing. On these subjects, he published more than 150 scientific papers in international journals, contributed volumes and conference proceedings. Claudio Zandron: He received Ph.D. in Computer Science at the University of Milan, Italy, in 2001. Since 2002 he is assistant professor at the University of Milano-Bicocca, Italy. He is member of the EATCS (European Association for Theoretical Computer Science) and of EMCC (European Molecular Computing Consortium). His research interests are Molecular Computing (DNA and Membrane Computing) and Formal Languages.