Abstract
In this paper we study the relative succinctness of different representations of deterministic polynomial time languages and investigate what can and cannot be formally verified about these representations. We also show that the relative succinctness of different representations of languages is directly related to the separation of the corresponding complexity classes; for example, PTIME ≠ NPTIME if and only if the relative succinctness of representing languages in PTIME by deterministic and nondeterministic clocked polynomial time machines is not recursively bounded, which happens if and only if the relative succinctness of these representations is not linearly bounded.
Furthermore, we discuss the problem of approximating the recognition of complete languages in NPTIME by deterministic polynomial time machines which accept finite initial segments of these languages. We conclude by discussing the relative succinctness of optimal and near-optimal programs and the nature of the families of minimal machines for different representations.
Research supported in part by National Science Foundation grant MCS 78-00418
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© 1979 Springer-Verlag Berlin Heidelberg
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Hartmanis, J., Baker, T.P. (1979). Relative succinctness of representations of languages and separation of complexity classes. In: Bečvář, J. (eds) Mathematical Foundations of Computer Science 1979. MFCS 1979. Lecture Notes in Computer Science, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09526-8_6
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DOI: https://doi.org/10.1007/3-540-09526-8_6
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