Toward a Searchable Space of Dynamical System Models
University of California, Irvine
In the spirit of exploring what is computationally possible with simple formal systems, one may try to identify spaces of formalized dynamical systems that possess both (1) demonstrated expressive power in scientific modeling and (2) representation as discrete labeled graph structures that can be searched and explored computationally. Possibly a third criterion is (3) self-applicability: useful transformations and searches of such dynamical systems should be expressible as discrete-time dynamical systems that compute. Dynamical grammars  (DGs) provide a space of dynamical system models composed of rewrite rules with algebraic rate laws, mapped to a semantics based on an algebra of stochastic processes. DGs have been used in modeling biological systems at the cellular and developmental levels; they can be represented as graphs with a lot of node types and labels; and they can express graph grammars and thereby transform other dynamical grammars. They could be further developed into a substrate for fundamental explorations of computation and dynamics.
 “Stochastic Process Semantics for Dynamical Grammar Syntax: An Overview”, Eric Mjolsness. Proceedings of the Ninth International Symposium on Artificial Intelligence and Mathematics, January 2006. www.arxiv.org/pdf/cs.AI/0511073.