Post Correspondence Problem: Primitivity and interrelations with complexity classes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)
We first introduce the notion of a general primality type, for a systematic study of “simple”, “primitive” or “prime” solutions of the Post Correspondence Problem. We give an exhaustive charcterization of general primality types. We then introduce PCP-related complexity classes, for instance, the time complexity classes PCP-P and PCP-NP. We obtain the chain of inclusions
$$P \subseteqq PCP - P \subseteqq PCP - NP = NP \subseteqq P - SPACE = PCP - P - SPACE = PCP - NP - SPACE.$$
KeywordsTarget Word Space Complexity Complexity Class Primality Type Fundamental Lemma
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© Springer-Verlag Berlin Heidelberg 1993