Abstract
Parallel Turing machines ( Ptm) can be viewed as a generalization of cellular automata ( Ca) where an additional measure called processor complexity can be defined which indicates the “amount of parallelism” used. In this paper Ptm are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as diagonalization are used to obtain hierarchies of complexity classes for Ptm and Ca. In some cases it is possible to keep the space complexity of Ptm fixed. Thus for the first time it is possible to find hierarchies of complexity classes (though not Ca classes) which are completely contained in the class of languages recognizable by Ca with space complexity n and in polynomial time. A possible collapse of the time hierarchy for these Ca would therefore also imply some unexpected properties of Ptm.
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