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Ambiguity and Communication

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Abstract

The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for inputs of size n. For every natural number k we construct a family \((L_{r}^{k}\;|\;r\in \mathbb{N})\) of languages which can be recognized by NFA’s with size k⋅poly(r) and ambiguity O(n k), but \(L_{r}^{k}\) has only NFA’s with size exponential in r, if ambiguity o(n k) is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, SIAM J. Comput. 19:1263–1282, 1989, Leung, SIAM J. Comput. 27:1073–1082, 1998).

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Authors and Affiliations

  1. Department of Computer Science, ETH Zürich, ETH Zentrum, 8022, Zürich, Switzerland

    Juraj Hromkovič

  2. Department of Computer Science, Johann-Wolfgang-Goethe Universität, Robert Mayer-Strasse 11-15, 60054, Frankfurt a. M., Germany

    Georg Schnitger

Authors
  1. Juraj Hromkovič
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  2. Georg Schnitger
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Correspondence to Georg Schnitger.

Additional information

Research supported by SNF-grant SNF-grant 200020-120073 and DFG-grant SCHN 503/4-1.

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Hromkovič, J., Schnitger, G. Ambiguity and Communication. Theory Comput Syst 48, 517–534 (2011). https://doi.org/10.1007/s00224-010-9277-4

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  • DOI: https://doi.org/10.1007/s00224-010-9277-4

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