Abstract
We introduce R-automata – finite state machines which operate on a finite number of unbounded counters. The values of the counters can be incremented, reset to zero, or left unchanged along the transitions. R-automata can be, for example, used to model systems with resources (modeled by the counters) which are consumed in small parts but which can be replenished at once. We define the language accepted by an R-automaton relative to a natural number D as the set of words allowing a run along which no counter value exceeds D. As the main result, we show decidability of the universality problem, i.e., the problem whether there is a number D such that the corresponding language is universal. We present a proof based on finite monoids and the factorization forest theorem. This theorem was applied for distance automata in [12]– a special case of R-automata with one counter which is never reset. As a second technical contribution, we extend the decidability result to R-automata with Büchi acceptance conditions.
This work has been partially supported by the EU CREDO project.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abdulla, P.A., Krcal, P., Yi, W.: Sampled universality of timed automata. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 2–16. Springer, Heidelberg (2007)
Abdulla, P.A., Krcal, P., Yi, W.: R-automata. Technical Report 2008-015, IT Department, Uppsala University (June 2008)
Bojańczyk, M., Colcombet, T.: Bounds in omega-regularity. In: Proc. of LICS 2006, pp. 285–296. IEEE Computer Society Press, Los Alamitos (2006)
Colcombet, T.: Factorisation forests for infinite words. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 226–237. Springer, Heidelberg (2007)
Colcombet, T., Löding, C.: The non-deterministic Mostowski hierarchy and distance-parity automata. In: Proc. of ICALP 2008. LNCS, vol. 5126, pp. 398–409. Springer, Heidelberg (2008)
Hashiguchi, K.: Limitedness theorem on finite automata with distance functions. Journal of Computer and System Sciences 24(2), 233–244 (1982)
Hashiguchi, K.: Improved limitedness theorems on finite automata with distance functions. Theoretical Computer Science 72(1), 27–38 (1990)
Kirsten, D.: Distance desert automata and the star height problem. Informatique Theorique et Applications 39(3), 455–509 (2005)
Krcal, P., Pelanek, R.: On sampled semantics of timed systems. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 310–321. Springer, Heidelberg (2005)
Leung, H.: Limitedness theorem on finite automata with distance functions: an algebraic proof. Theoretical Computer Science 81(1), 137–145 (1991)
Simon, I.: Factorization forests of finite height. Theoretical Computer Science 72(1), 65–94 (1990)
Simon, I.: On semigroups of matrices over the tropical semiring. Informatique Theorique et Applications 28(3-4), 277–294 (1994)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abdulla, P.A., Krcal, P., Yi, W. (2008). R-Automata. In: van Breugel, F., Chechik, M. (eds) CONCUR 2008 - Concurrency Theory. CONCUR 2008. Lecture Notes in Computer Science, vol 5201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85361-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-85361-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85360-2
Online ISBN: 978-3-540-85361-9
eBook Packages: Computer ScienceComputer Science (R0)