The complexity of dynamic languages and dynamic optimization problems

In this paper we offer a unifying framework for dynamic problems in terms of “dynamic languages”, and we discuss the complexity of these languages. In particular, many dynamic languages derived from NP-complete languages can be shown to be polynomial space (P-space) complete. Among these are the following: the dynamic 3-satisfiability problem, and dynamic 3-dimensional matching problem, the dynamic partition problem, the dynamic hamiltonian circuit problem, and the dynamic independent set problem. We provide a general technique for showing how to prove the P-space completeness of dynamic problems derived from NP-complete problems.