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Some Decision Questions Concerning the Time Complexity of Language Acceptors

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Developments in Language Theory (DLT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

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Abstract

Almost all the decision questions concerning the resource requirements of a computational device are undecidable. Here we want to understand the exact boundary that separates the undecidable from the decidable cases of such problems by considering the time complexity of very simple devices that include NFAs (1-way and 2-way), NPDAs and NPDAs augmented with counters - and their unambiguous restrictions. We consider several variations - based on whether the bound holds exactly or as an upper-bound and show decidability as well as undecidability results. We also introduce a stronger version of machine equivalence (known as run-time equivalence) and identify classes of machines for which run-time equivalence is decidable (undecidable). In the case of decidable problems, we also attempt to determine more precisely the complexity class to which the problem belongs.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. Department of Computer & Engineering Science, Sonoma State University, Rohnert Park, CA, 94928, USA

    Bala Ravikumar

Authors
  1. Oscar H. Ibarra
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  2. Bala Ravikumar
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Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

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Ibarra, O.H., Ravikumar, B. (2013). Some Decision Questions Concerning the Time Complexity of Language Acceptors. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_24

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  • DOI: https://doi.org/10.1007/978-3-642-38771-5_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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