Hostname: page-component-6bf8c574d5-j5c6p Total loading time: 0 Render date: 2025-03-09T23:06:49.633Z Has data issue: false hasContentIssue false
  • English
  • Français

Weighted synchronous automata

Published online by Cambridge University Press:  25 January 2023

Leandro Gomes Open the ORCID record for Leandro Gomes [Opens in a new window] ,
Alexandre Madeira  and
Luis Soares Barbosa
Leandro Gomes*
Affiliation:
Université de Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
Alexandre Madeira
Affiliation:
CIDMA, University of Aveiro, Aveiro, Portugal
Luis Soares Barbosa
Affiliation:
HASLab INESC TEC, University of Minho, INL, Braga, Portugal
*
*Corresponding author. Email: leandrogomes.moreiragomes@univ-lille.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper introduces a class of automata and associated languages, suitable to model a computational paradigm of fuzzy systems, in which both vagueness and simultaneity are taken as first-class citizens. This requires a weighted semantics for transitions and a precise notion of a synchronous product to enforce the simultaneous occurrence of actions. The usual relationships between automata and languages are revisited in this setting, including a specific Kleene theorem.

Keywords

Weighted automataregular languagessynchronous languages
Type
Special Issue: LSFA’19 and LSFA’20
Information
Mathematical Structures in Computer Science , Volume 32 , Special Issue 9: LSFA 2019 and 2020 , October 2022 , pp. 1234 - 1253
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

This work is financed by the FCT – Fundação para a Ciência e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within the project IBEX, with reference PTDC/CCI-COM/4280/2021 and project UIDB/04106/2020.

References

Bollig, B., Gastin, P., Monmege, B. and Zeitoun, M. (2012). A probabilistic Kleene theorem. In: Chakraborty, S. and Mukund, M. (eds.) Automated Technology for Verification and Analysis, LNCS, vol. 7561, Springer Berlin Heidelberg, 400–415.CrossRefGoogle Scholar
Broda, S., Machiavelo, A., Moreira, N. and Reis, R. (2013). On the average size of glushkov and equation automata for KAT expressions. In: Gasieniec, L. and Wolter, F. (eds.) Fundamentals of Computation Theory - 19th International Symposium, FCT 2013, Liverpool, UK, August 19–21, 2013. Proceedings, Lecture Notes in Computer Science, vol. 8070, Springer, 72–83.CrossRefGoogle Scholar
de Bruin, J. S., Schuh, C. J., Rappelsberger, A. and Adlassnig, K.-P. (2018). Medical fuzzy control systems with fuzzy arden syntax. In: Kacprzyk, J., Szmidt, E., Zadrozny, S., Atanassov, K. T. and Krawczak, M. (eds.) Advances in Fuzzy Logic and Technology 2017 - Proceedings of: EUSFLAT-2017 - The 10th Conference of the European Society for Fuzzy Logic and Technology, 2017, Warsaw, Poland IWIFSGN’2017 - The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, 2017, Warsaw, Poland, Volume 1, Advances in Intelligent Systems and Computing, vol. 641, Cham, Springer, 574–584.CrossRefGoogle Scholar
Doostfatemeh, M. and Kremer, S. C. (2005). New directions in fuzzy automata. International Journal of Approximate Reasoning 38 (2) 175–214.CrossRefGoogle Scholar
Gomes, L., Madeira, A. and Barbosa, L. S. (2020). Introducing synchrony in fuzzy automata. ENTCS 348 43–60. (LSFA 2019).Google Scholar
Gomes, L., Madeira, A. and Barbosa, L. S. (2021). A semantics and a logic for fuzzy arden syntax. Soft Computing 25 (9) 6789–6805.CrossRefGoogle Scholar
Hoare, T., Möller, B., Struth, G. and Wehrman, I. (2011). Concurrent Kleene algebra and its foundations. Journal of Logical and Algebraic Methods in Programming 80 (6) 266–296.CrossRefGoogle Scholar
Hopcroft, J. E., Motwani, R. and Ullman, J. D. (2003). Introduction to Automata Theory, Languages, and Computation, int. ed. 2nd ed., Addison-Wesley.Google Scholar
Hopcroft, J. E. and Ullman, J. D. (1979). Introduction to Automata Theory, Languages, and Computation, Addison-Wesley Publishing Company.Google Scholar
Jipsen, P. and Andrew Moshier, M. (2016). Concurrent kleene algebra with tests and branching automata. Journal of Logical and Algebraic Methods in Programming 85 (4) 637–652.CrossRefGoogle Scholar
Kleene, S. C. (1956). Representation of events in nerve nets and finite automata. In: Shannon, C. and McCarthy, J. (eds.) Automata Studies, Princeton, NJ, Princeton University Press, 3–41.Google Scholar
Kozen, D. and Mamouras, K. (2014). Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) CSL-LICS, ACM, vol. 44, 1–10.Google Scholar
Kozen, D. (1990). On Kleene algebras and closed semirings. In: Rovan, B. (ed.) Mathematical Foundations of Computer Science 1990, Czechoslovakia, 1990, Proc., LNCS, vol. 452, Springer, 26–47.CrossRefGoogle Scholar
Kozen, D. (1997). Kleene algebra with tests. ACM Transactions on Programming Languages and Systems 19 (3) 427–443.CrossRefGoogle Scholar
Lee, E. T. and Zadeh, L. A. (1969). Note on fuzzy languages. Information Sciences 1 (4) 421–434.CrossRefGoogle Scholar
Li, Y. and Pedrycz, W. (2005). Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids. Fuzzy Sets and Systems 156 (1) 68–92.CrossRefGoogle Scholar
Liu, A., Wang, S., Barbosa, L. S. and Sun, M. (2021). Fuzzy automata as coalgebras. Mathematics 9 (3) 272.CrossRefGoogle Scholar
Lin, F. and Ying, H. (2002). Modeling and control of fuzzy discrete event systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B 32 (4) 408–415.Google ScholarPubMed
Mateescu, A., Salomaa, A., Salomaa, K. and Yu, S. (1995). Lexical analysis with a simple finite-fuzzy-automaton model. Journal of UCS 1 (5) 292–311.Google Scholar
McIver, A., Cohen, E. and Morgan, C. (2006). Using probabilistic kleene algebra for protocol verification. In: Schmidt, R. A. (ed.) Relations and Kleene Algebra in Computer Science, 9th International Conference on Relational Methods in Computer Science and 4th International Workshop on Applications of Kleene Algebra, RelMiCS/AKA 2006, Manchester, UK, August 29–September 2, 2006, Proceedings, Lecture Notes in Computer Science, vol. 4136, Springer, 296–310.CrossRefGoogle Scholar
McIver, A., Rabehaja, T. M. and Struth, G. (2013). Probabilistic concurrent Kleene algebra. In: Bortolussi, L. and Wiklicky, H. (eds.) QAPL 2013, Italy, EPTCS, vol. 117, 97–115.CrossRefGoogle Scholar
McIver, A., Rabehaja, T. and Struth, G. (2016). Probabilistic rely-guarantee calculus. Theoretical Computer Science 655 120–134. QAPL (2013-14).CrossRefGoogle Scholar
Milner, R. (1980). A Calculus of Communicating Systems. Springer Lecture Notes in Computer Science, vol. 92, Springer-Verlag.Google Scholar
Milner, R. (1983). Calculi for synchrony and asynchrony. Theoretical Computer Science 25 267–310.CrossRefGoogle Scholar
Milner, R. (2006). Turing, Computing and Communication. Springer Berlin Heidelberg, 1–8.Google Scholar
Mordeson, J. and Malik, D. (2002). Fuzzy Automata and Languages: Theory and Applications, 1st ed., Chapman and Hall/CRC.CrossRefGoogle Scholar
Owicki, S. and Gries, D. (1976). An axiomatic proof technique for parallel programs I. Acta Informatica 6 (4) 319–340.CrossRefGoogle Scholar
Pedrycz, W. and Gacek, A. (2001). Learning of fuzzy automata. International Journal of Computational Intelligence and Applications 1 (1) 19–33.CrossRefGoogle Scholar
Prisacariu, C. (2010). Synchronous Kleene algebra. Journal of Logical and Algebraic Methods in Programming 79 (7) 608–635.CrossRefGoogle Scholar
Qiao, R., Wu, J., Wang, Y. and Gao, X. (2008). Operational semantics of probabilistic Kleene algebra with tests. In: Proceedings - IEEE Symposium on Computers and Communications, 706–713.Google Scholar
Rabin, M. O. (1963). Probabilistic automata. Information and Control 6 (3) 230–245.CrossRefGoogle Scholar
Segerberg, K. (1982). A deontic logic of action. Studia Logica 41 (2) 269–282.CrossRefGoogle Scholar
Thiemann, P. (ed.) (2016). Programming Languages and Systems - 25th European Symposium on Programming, ESOP 2016, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2–8, 2016, Proceedings, Lecture Notes in Computer Science, vol. 9632, Springer.Google Scholar
Vidal, E., Thollard, F., de la Higuera, C., Casacuberta, F. and Carrasco, R. C. (2005a). Probabilistic finite-state machines-part I. IEEE Transactions on Pattern Analysis and Machine Intelligence 27 (7) 1013–1025.CrossRefGoogle ScholarPubMed
Vidal, E., Thollard, F., de la Higuera, C., Casacuberta, F. and Carrasco, R. C. (2005b). Probabilistic finite-state machines - part II. IEEE Transactions on Pattern Analysis and Machine Intelligence 27 (7) 1026–1039.CrossRefGoogle ScholarPubMed
von Wright, G. H. (1968). An Essay in Deontic Logic and the General Theory of Action with a Bibliography of Deontic and Imperative Logic. –. North-Holland Pub. Co.Google Scholar
Wee, W. and Fu, K. S. (1969). A formulation of fuzzy automata and its application as a model of learning systems. IEEE Transactions on Systems, Man, and Cybernetics: Systems 5 215–223.Google Scholar
Ying, M. (2002). A formal model of computing with words. IEEE Transactions on Fuzzy Systems 10 (5) 640–652.CrossRefGoogle Scholar
Zadeh, L. A. (1996). Fuzzy languages and their relation to human and machine intelligence. In: Proceedings of International Conference on Man and Computer, 148–179.CrossRefGoogle Scholar