Abstract
Hertrampf et al. (1993) looked at complexity classes which are characterized (say accepted) by a regular language for the words of output bits produced by nondeterministic polynomial-time computations. A number of well-known complexity classes between P and PSPACE are accepted by regular languages. For example, NP is accepted by the regular language which consists of the words which contain at least one letter 1. The main result will be that the inclusion order on the complexity classes accepted by regular languages has the following property: if a class accepted by a nontrivial regular language is not equal to P then it contains at least one of the classes NP, co-NP and MOD p P for p prime. This will be interpreted as a nondensity result in two ways: 1. (1)on the assumption that the polynomial-time hierarchy does not collapse, 2. (2)for the relativized case.
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