Equivalence Checking Problem for Finite State Transducers over Semigroups

  • Vladimir A. ZakharovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9270)


Finite state transducers over semigroups can be regarded as a formal model of sequential reactive programs. In this paper we introduce a uniform technique for checking effectively functionality, k-valuedness, equivalence and inclusion for this model of computation in the case when a semigroup these transducers operate over is embeddable in a decidable group.


Source Node Decidable Group Word Problem Equivalence Problem Equivalence Check 
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  1. 1.
    Alur, R., Cerny, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: Proc. of 38th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pp. 599–610 (2011)Google Scholar
  2. 2.
    Blattner, M., Head, T.: Single-valued a-transducers. Journal of Computer and System Sciences 15, 310–327 (1977)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Blattner, M., Head, T.: The decidability of equivalence for deterministic finite transducers. Journal of Computer and System Sciences 19, 45–49 (1979)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Beal, M.-P., Carton, O., Prieur, C., Sakarovitch, J.: Squaring transducers: an efficient procedure for deciding functionality and sequentiality. Theoretical Computer Science 292 (2003)Google Scholar
  5. 5.
    Culik, K., Karhumaki, J.: The equivalence of finite-valued transducers (on HDTOL languages) is decidable. Theoretical Computer Science 47, 71–84 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Griffiths, T.: The unsolvability of the equivalence problem for \(\varepsilon \)-free nondeterministic generalized machines. Journal of the ACM 15, 409–413 (1968)zbMATHCrossRefGoogle Scholar
  7. 7.
    Gurari, E., Ibarra, O.: A note on finite-valued and finitely ambiguous transducers. Mathematical Systems Theory 16, 61–66 (1983)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Ibarra, O.: The unsolvability of the equivalence problem for Efree NGSM’s with unary input (output) alphabet and applications. SIAM Journal on Computing 4 (1978)Google Scholar
  9. 9.
    Malcev, A.I.: Uber die Einbettung von assoziativen Systemen. Gruppen, Rec. Math. (Mat. Sbornik) N.S. 6, 331–336 (1939)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Veanes, M., Hooimeijer, P., Livshits, B., et al.: Symbolic finite state transducers: algorithms and applications. In: Proc. of the 39th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages (2012)Google Scholar
  11. 11.
    Sakarovitch, J., de Souza, R.: On the decomposition of k-valued rational relations. In: Proc. of 25th International Symposium on Theoretical Aspects of Computer Science, pp. 621–632 (2008)Google Scholar
  12. 12.
    Sakarovitch, J., de Souza, R.: On the decidability of bounded valuedness for transducers. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 588–600. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  13. 13.
    Schutzenberger, M.P.: Sur les relations rationnelles. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 209–213. Springer, Heidelberg (1975) Google Scholar
  14. 14.
    de Souza, R.: On the decidability of the equivalence for k-valued transducers. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 252–263. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  15. 15.
    Weber, A.: On the valuedness of finite transducers. Acta Informatica 27, 749–780 (1989)Google Scholar
  16. 16.
    Weber, A.: Decomposing finite-valued transducers and deciding their equivalence. SIAM Journal on Computing 22, 175–202 (1993)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Zakharov, V.A.: An efficient and unified approach to the decidability of equivalence of propositional program schemes. In: Proc. of the 25th International Colloquium “Automata, Languages and Programming”, pp. 247–258 (1998)Google Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute for System Programming RASNational Research University Higher School of EconomicsMoscowRussia

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