Abstract
This paper reports on the work done for the implementation of the algorithms for the computation of the minimal quotient of an automaton in the Awali platform. In the case of non-deterministic or of weighted automata, the minimal quotient of an automaton is obtained by merging all states in bisimulation. Two strategies are explored for the computation of the coarsest bisimulation equivalence. The first one is an extension of the Moore algorithm for the computation of the minimal quotient of a DFA; the second one is inspired by the Hopcroft algorithm for the same problem. These two strategies yield algorithms with the same quadratic complexity and we study the cases where the second strategy can be improved in order to achieve a complexity similar to the one of Hopcroft algorithm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Called sequential in [10].
References
Béal, M.P., Crochemore, M.: Minimizing incomplete automata. In: Finite-State Methods and Natural Language Processing FSMNLP 2008, pp. 9–16 (2008)
Béal, M.-P., Lombardy, S., Sakarovitch, J.: Conjugacy and equivalence of weighted automata and functional transducers. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 58–69. Springer, Heidelberg (2006). https://doi.org/10.1007/11753728_9
Berstel, J., Boasson, L., Carton, O., Fagnot, I.: Minimization of automata. In: Pin, J.E. (ed.) Automata: From Mathematics to Applications (to appear). arXiv:1010.5318v3
Berstel, J., Carton, O.: On the complexity of Hopcroft’s state minimization algorithm. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 35–44. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30500-2_4
Castiglione, G., Restivo, A., Sciortino, M.: On extremal cases of Hopcroft’s algorithm. Theor. Comput. Sci. 411(38–39), 3414–3422 (2010)
Gries, D.: Describing an algorithm by Hopcroft. Acta Informatica 2, 97–109 (1973)
Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation, 3rd edn. Addison-Wesley, Boston (2006)
Paige, R.: Efficient translation of external input in a dynamically typed language. In: Technology and Foundations - Information Processing IFIP 1994, IFIP Transactions, vol. A-51, pp. 603–608. North-Holland (1994)
Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)
Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press, New York (2009)
Valmari, A., Lehtinen, P.: Efficient minimization of DFAs with partial transition. In: STACS 2008, LIPIcs, vol. 1, pp. 645–656. Schloss Dagstuhl (2008)
Awali: Another Weighted Automata LIbrary. vaucanson-project.org/AWALI
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Lombardy, S., Sakarovitch, J. (2018). Two Routes to Automata Minimization and the Ways to Reach It Efficiently. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_21
Download citation
DOI: https://doi.org/10.1007/978-3-319-94812-6_21
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94811-9
Online ISBN: 978-3-319-94812-6
eBook Packages: Computer ScienceComputer Science (R0)