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Relative succinctness of representations of languages and separation of complexity classes

  • Juris Hartmanis
  • T. P. Baker
Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 74)

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.

Keywords

Polynomial Time Turing Machine Nomial Time Minimal Machine Deterministic Polynomial Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Juris Hartmanis
    • 1
  • T. P. Baker
    • 2
  1. 1.Department of Computer ScienceCornell UniversityIthaca
  2. 2.Department of Computer ScienceUniversity of IowaIowa City

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