Two-Way Automata over Locally Finite Semirings

  • Louis-Marie Dando
  • Sylvain LombardyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)


Two-way transducers or weighted automata are in general more powerful than one-way ones. We show that two-way automata over locally finite semirings may have undefined behaviour. We prove that it is decidable whether this behaviour is defined, and, if it is, we show that two-way automata over locally finite semirings are equivalent to one-way automata.


  1. 1.
    Birget, J.C.: Concatenation of inputs in a two-way automaton. Theor. Comput. Sci. 63(2), 141–156 (1989). Scholar
  2. 2.
    Carnino, V., Lombardy, S.: On determinism and unambiguity of weighted two-way automata. In: AFL 2014. EPTCS, vol. 151, pp. 188–200 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Engelfriet, J., Hoogeboom, H.J.: MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Log. 2(2), 216–254 (2001)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Leung, H.: Limitedness theorem on finite automata with distance functions: an algebraic proof. Theor. Comput. Sci. 81(1, (Part A)), 137–145 (1991)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lombardy, S.: Weighted two-way automata. In: NCMA 2015., vol. 318, pp. 37–47. Österreichische Computer Gesellschaft (2015)Google Scholar
  6. 6.
    Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 114–125 (1959). Scholar
  7. 7.
    Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3(2), 198–200 (1959). Scholar

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© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.LaBRI UMR 5800, Université de Bordeaux, INP Bordeaux, CNRSBordeauxFrance

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