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On the Computational Power of Affine Automata

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10168)

Abstract

We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.

Keywords

  • Non-classical models of automata
  • Affine automata
  • Cutpoint languages
  • Bounded error
  • Compact sets
  • Error reduction

M. Hirvensalo—Partially supported by Väisälä Foundation.

E. Moutot—Partially supported by TUCS COM\({}^3\)-project and ANR project CoCoGro (ANR-16-CE40-0005).

A. Yakaryılmaz—Partially supported by TUCS COM\({}^3\)-project and ERC Advanced Grant MQC.

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Correspondence to Mika Hirvensalo , Etienne Moutot or Abuzer Yakaryılmaz .

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Hirvensalo, M., Moutot, E., Yakaryılmaz, A. (2017). On the Computational Power of Affine Automata. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_30

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_30

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