Relative succinctness of representations of languages and separation of complexity classes
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.
KeywordsPolynomial Time Turing Machine Nomial Time Minimal Machine Deterministic Polynomial Time
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- 1.Aho, A.V., J.E. Hopcroft and J.D. Ullman, "The Design and Analysis of Computer Algorithms," Addison-Wesley, Reading, Massachusetts, 1974.Google Scholar
- 2.Baker, T.P., "On "Provable" Analogs of P and NP," Mathematical Systems Theory (to appear).Google Scholar
- 5.Hartmanis, J., "On the Succinctness of Different Representations of Languages," SIAM J. Computing (to appear).Google Scholar
- 6.Hartmanis, J. and J. Simon., "On the Structure of Feasible Computations," Advances in Computers Vol. 14, Morris Rubinoff and Marshall C. Yovits, eds., 1–43, Academic Press, New York, 1976.Google Scholar
- 7.Levin, L.A., "Universal Sequential Search Problems," Problemy Peredachi Informatsii, Vol. 9 (1973), 265–266.Google Scholar
- 9.Meyer, A.R. and M.J. Fischer., "Economy of Description by Automata, Grammars and Formal Systems," Conference Record IEEE 12th Annual Symposium on Switching and Automata Theory (1971), 188–190.Google Scholar