Parallel complexity of iterated morphisms and the arithmetic of small numbers
We improve several upper bounds to the complexity of the membership problem for languages defined by iterated morphisms (D0L systems). The complexity bounds are expressed in terms of DLOGTIME-uniform circuit families. We prove: 1) For polynomially growing DOL systems the membership problem is contained in AC 0. 2) For arbitrary DOL systems the membership problem is contained in NC 1. 3) The latter can be improved to TC 0 if and only if upper bounds to a number of natural arithmetic problems can be improved to TC 0. 4) The general D0L membership problem (the D0L system is part of the input) is contained in Cook's class DET.
KeywordsArithmetic Problem Membership Problem Boolean Circuit Circuit Family Derivation Length
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