Abstract
Our aim is to present an efficient algorithm for checking whether a regular language is geometrical or not, based on specific properties of its minimal automaton. Geometrical languages have interesting theoretical properties and they provide an original model for off-line temporal validation of real-time softwares. As far as implementation is concerned, the regular case is of practical interest, which motivates the design of an efficient geometricity test addressing the family of regular languages. This study generalizes the algorithm designed by the authors for the case of prolongable binary regular languages.
Keywords
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
Baruah, S.K., Rosier, L.E., Howell, R.R.: Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor. Real-Time Systems 2(4), 301–324 (1990)
Blanpain, B., Champarnaud, J.M., Dubernard, J.P.: Geometrical languages. In: Vide, C.M. (ed.) International Conference on Language Theory and Automata (LATA 2007). GRLMC Universitat Rovira I Virgili, vol. 35 (2007)
Champarnaud, J.M., Dubernard, J.P., Jeanne, H.: An efficient algorithm to test whether a binary and prolongeable regular language is geometrical. Int. J. Found. Comput. Sci. 20(4), 763–774 (2009)
Eilenberg, S.: Automata, languages and machines, vol. B. Academic Press, New York (1976)
Geniet, D., Largeteau, G.: Wcet free time analysis of hard real-time systems on multiprocessors: A regular language-based model. Theor. Comput. Sci. 388(1-3), 26–52 (2007)
Kleene, S.: Representation of events in nerve nets and finite automata. Automata Studies Ann. Math. Studies 34, 3–41 (1956)
Largeteau-Skapin, G., Geniet, D., Andres, E.: Discrete geometry applied in hard real-time systems validation. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 23–33. Springer, Heidelberg (2005)
Myhill, J.: Finite automata and the representation of events. WADD TR-57-624, 112–137 (1957)
Nerode, A.: Linear automata transformation. Proceedings of AMS 9, 541–544 (1958)
Parikh, R.: On context-free languages. J. ACM 13(4), 570–581 (1966)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Champarnaud, JM., Dubernard, JP., Jeanne, H. (2010). Geometricity of Binary Regular Languages. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-13089-2_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13088-5
Online ISBN: 978-3-642-13089-2
eBook Packages: Computer ScienceComputer Science (R0)