Abstract
We address the problem of providing a Borel-like classification of languages of infinite Mazurkiewicz traces, and provide a solution in the framework of ω-automata over infinite words – which is invoked via the sets of linearizations of infinitary trace languages. We identify trace languages whose linearizations are recognized by deterministic weak or deterministic Büchi (word) automata. We present a characterization of the class of linearizations of all recognizable ω-trace languages in terms of Muller (word) automata. Finally, we show that the linearization of any recognizable ω-trace language can be expressed as a Boolean combination of languages recognized by our class of deterministic Büchi automata.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chaturvedi, N.: Toward a Structure Theory of Regular Infinitary Trace Languages. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 134–145. Springer, Heidelberg (2014)
Diekert, V., Muscholl, A.: Deterministic Asynchronous Automata for Infinite Traces. Acta Informatica 31(4), 379–397 (1994)
Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific (1995)
Gastin, P., Petit, A.: Asynchronous Cellular Automata for Infinite Traces. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 583–594. Springer, Heidelberg (1992)
Löding, C.: Efficient minimization of deterministic weak ω-automata. Information Processing Letters 79(3), 105–109 (2001)
Madhavan, M.: Automata on Distributed Alphabets. In: D’Souza, D., Shankar, P. (eds.) Modern Applications of Automata Theory. IISc Research Monographs Series, vol. 2, pp. 257–288. World Scientific (May 2012)
Mazurkiewicz, A.: Trace Theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) Petri Nets: Applications and Relationships to Other Models of Concurrency. LNCS, vol. 255, pp. 278–324. Springer, Heidelberg (1987)
Muscholl, A.: Über die Erkennbarkeit unendlicher Spuren. PhD thesis (1994)
Perrinand., D., Pin, J.-É.: Automata and Infinite Words. In: Infinite Words: Automata, Semigroups, Logic and Games. Pure and Applied Mathematics, vol. 141. Elsevier (2004)
Staiger, L.: Subspaces of GF(q)ω and Convolutional Codes. Information and Control 59(1-3), 148–183 (1983)
Zielonka, W.: Notes on Finite Asynchronous Automata. R.A.I.R.O. – Informatique Théorique et Applications 21, 99–135 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag GmbH Berlin Heidelberg
About this paper
Cite this paper
Chaturvedi, N., Gelderie, M. (2014). Classifying Recognizable Infinitary Trace Languages Using Word Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_15
Download citation
DOI: https://doi.org/10.1007/978-3-662-44522-8_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44521-1
Online ISBN: 978-3-662-44522-8
eBook Packages: Computer ScienceComputer Science (R0)