Efficient Universal Pushdown Cellular Automata and Their Application to Complexity

In order to obtain universal classical cellular automata an in nite space is required. Therefore, the number of required processors depends on the length of input data and, additionally, may increase during the computation. On the other hand, Turing machines are universal devices which have one processor only and additionally an in nite storage tape. Here an in some sense intermediate model is studied. The pushdown cellular automata are a stack augmented generalization of classical cellular automata. They form a massively parallel universal model where the number of processors is bounded by the length of input data. E cient universal pushdown cellular automata and their e ciently veri able encodings are proposed. They are applied to computational complexity, and tight time and stack-space hierarchies are shown. CR Subject Classi cation (1998): F.1, F.4.3, B.6.1, E.1 E-mail: [email protected] Copyright c 2000 by the author