Abstract
We define an extension of forest algebra for ω-forests. We show how the standard algebraic notions (free object, syntactic algebra, morphisms, etc.) extend to the infinite case. To prove its usefulness, we use the framework to get an effective characterization of the ω-forest languages that are definable in the temporal logic that uses the operator EF (exists finally).
Work partially funded by the Polish government grant no. N206 008 32/0810.
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
Preview
Unable to display preview. Download preview PDF.
References
Benedikt, M., Segoufin, L.: Regular tree languages definable in FO. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 327–339. Springer, Heidelberg (2005); A revised version, correcting an error from the conference paper, www.lsv.ens-cachan.fr/~segoufin/Papers/
Blumensath, A.: Recognisability for algebras of infinite trees (unpublished, 2009)
Bojańczyk, M.: Two-way unary temporal logic over trees. In: Logic in Computer Science, pp. 121–130 (2007)
Bojańczyk, M.: Effective characterizations of tree logics. In: PODS, pp. 53–66 (2008)
Bojańczyk, M., Segoufin, L.: Tree languages defined in first-order logic with one quantifier alternation. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 233–245. Springer, Heidelberg (2008)
Bojańczyk, M., Segoufin, L., Straubing, H.: Piecewise testable tree languages. In: Logic in Computer Science, pp. 442–451 (2008)
Bojańczyk, M., Walukiewicz, I.: Characterizing EF and EX tree logics. Theoretical Computer Science 358(2-3), 255–273 (2006)
Bojańczyk, M., Walukiewicz, I.: Forest algebras. In: Automata and Logic: History and Perspectives, pp. 107–132. Amsterdam University Press (2007)
Eilenberg, S.: Automata, Languages and Machines, vol. B. Academic Press, New York (1976)
Perrin, D., Pin, J.-É.: Infinite Words. Elsevier, Amsterdam (2004)
Wilke, T.: An algebraic theory for languages of finite and infinite words. Inf. J. Alg. Comput. 3, 447–489 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bojańczyk, M., Idziaszek, T. (2009). Algebra for Infinite Forests with an Application to the Temporal Logic EF. In: Bravetti, M., Zavattaro, G. (eds) CONCUR 2009 - Concurrency Theory. CONCUR 2009. Lecture Notes in Computer Science, vol 5710. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04081-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-04081-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04080-1
Online ISBN: 978-3-642-04081-8
eBook Packages: Computer ScienceComputer Science (R0)