Complexity of bio-computation: Symbolic dynamics in membrane systems

We discuss aspects of biological relevance to the modelling of bio-computation in a multiset rewriting system context: turnover, robustness against perturbations, and the dataflow programming paradigm. The systems under consideration are maximally parallel and asynchronous parallel membrane systems, the latter corresponding to computation in which the notion of time is operationally meaningless. A natural geometrical setting which seems promising for the study of computational processes in general multiset rewriting systems is presented. Configuration space corresponds and state transitions correspond to vector to a subset of the lattice N-0(d),d is an element of N, addition. The similarities and differences with Vector Addition Systems and Petri nets are discussed. Symbolic dynamics are introduced on special partitions of configuration space and we indicate different notions of complexity for membrane systems based on this and related concepts such as graph complexity and minimal automata. Some examples of synchronized, pipelined dataflow computations are given and decompositions into functional subunits are briefly commented on.