Stochastic Evolution via Graph Grammars

This is the second part in the series of papers where we are looking for new connections between computer science, mathematics and physics. These connections go through the central notions of computer science grammar and graph grammar. In section 2 main de nitions concerning random graph grammars are given. Section 3 and 4 are devoted to the simplest models of graph dynamics: we study the large time behaviour of local and global characteristics of growing one-dimensional complexes. Main emphasis is on looking for correct problems and models, discussing their qualitative behaviour. We consider asymptotic growth of the number of connected components, the degree of local compactness, topological chaos, phases of di erent topology etc. In section 4 we construct in nite cluster dynamics. We discuss some aspects which distinguish thermodynamic limit for graph grammars from that for Gibbs elds on a lattice. One of the central emerging notions is the statistically homogeneous in nite complex. Key-words: Graph Grammar, Random Graph, Random Topology, Branching Process