Inapproximability of Nondeterministic State and Transition Complexity Assuming P ≠ NP

  • Hermann Gruber
  • Markus Holzer
Conference paper

DOI: 10.1007/978-3-540-73208-2_21

Volume 4588 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Gruber H., Holzer M. (2007) Inapproximability of Nondeterministic State and Transition Complexity Assuming P ≠ NP. In: Harju T., Karhumäki J., Lepistö A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg

Abstract

Inapproximability results concerning minimization of nondeterministic finite automata relative to given deterministic finite automata were obtained only recently, modulo cryptographic assumptions [4]. Here we give upper and lower bounds on the approximability of this problem utilizing only the common assumption P ≠ NP, in the setup where the input is a finite language specified by a truth table. To this end, we derive an improved inapproximability result for the biclique edge cover problem. The obtained lower bounds on approximability can be sharpened in the case where the input is given as a deterministic finite automaton over a binary alphabet. This settles most of the open problems stated in [4]. Note that the biclique edge cover problem was recently studied by the authors as lower bound method for the nondeterministic state complexity of finite automata [5].

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hermann Gruber
    • 1
  • Markus Holzer
    • 2
  1. 1.Institut für Informatik, Ludwig-Maximilians-Universität München, Oettingenstraße 67, D-80538 MünchenGermany
  2. 2.Institut für Informatik, Technische Universität München, Boltzmannstraße 3, D-85748 Garching bei MünchenGermany