Some Decision Questions Concerning the Time Complexity of Language Acceptors

Almost all the decision questions concerning the resource requirements of a computational device are undecidable. Here we want to understand the exact boundary that separates the undecidable from the decidable cases of such problems by considering the time complexity of very simple devices that include NFAs (1-way and 2-way), NPDAs and NPDAs augmented with counters - and their unambiguous restrictions. We consider several variations - based on whether the bound holds exactly or as an upper-bound and show decidability as well as undecidability results. We also introduce a stronger version of machine equivalence (known as run-time equivalence) and identify classes of machines for which run-time equivalence is decidable (undecidable). In the case of decidable problems, we also attempt to determine more precisely the complexity class to which the problem belongs.

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