Abstract
Given a timed regular expression and a dense-time Boolean signal we compute the set of all matches of the expression in the signal, that is, the set of all segments of the signal that satisfy the regular expression. The set of matches is viewed as a set of points in a two-dimensional space with each point indicating the beginning and end of a matching segment on the real time axis. Our procedure, which works by induction on the structure of the expression, is based on the following result that we prove in this paper: the set of all matches of a timed regular expression by a signal of finite variability and duration can be written as a finite union of zones.
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
Asarin, E., Caspi, P., Maler, O.: Timed regular expressions. Journal of the ACM (JACM) 49(2), 172–206 (2002)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. Journal of the ACM (JACM) 43(1), 116–146 (1996)
Altschul, S., Gish, W., Miller, W., Myers, E., Lipman, D.: Basic local alignment search tool. Journal of Molecular Biology, 403–410 (1990)
Bozga, M., Graf, S., Mounier, L.: IF-2.0: A validation environment for component-based real-time systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 343–348. Springer, Heidelberg (2002)
Boyer, R.S., Moore, J.S.: A fast string searching algorithm. Communications of the ACM (1977)
Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific (2002)
Cohen, B., Venkataramanan, S., Kumari, A.: Using PSL/Sugar for formal and dynamic verification: Guide to Property Specification Language for Assertion-based Verification. VhdlCohen Publishing (2004)
Dluhos, P., Brim, L., Safránek, D.: On expressing and monitoring oscillatory dynamics. In: HSB, pp. 73–87 (2012)
Eisner, C., Fisman, D.: A practical introduction to PSL. Springer (2006)
Friedl, J.: Mastering regular expressions. O’Reilly Media, Inc. (2006)
Faloutsos, C., Ranganathan, M., Manolopoulos, Y.: Fast subsequence matching in time-series databases. In: Proceedings of the ACM SIGMOD Conference on Management of Data (1994)
Havlicek, J., Little, S.: Realtime regular expressions for analog and mixed-signal assertions. In: FMCAD, pp. 155–162 (2011)
Jacox, E.H., Samet, H.: Spatial join techniques. ACM Transactions on Database Systems (TODS), 70 (2007)
Kleene, S.C.: Representation of events in nerve nets and finite automata. Automata Studies (1956)
Knuth, D.E., Morris Jr., J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM Journal on Computing, 323–350 (1977)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)
Laurikari, V.: NFAs with tagged transitions, their conversion to deterministic automata and application to regular expressions. In: Proceecedings of the Symposium on String Processing and Information Retrieval (SPIRE 2000), pp. 181–187 (2000)
Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT 2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004)
Maler, O., Nickovic, D., Pnueli, A.: Real time temporal logic: Past, present, future. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 2–16. Springer, Heidelberg (2005)
Maler, O., Ničković, D., Pnueli, A.: Checking temporal properties of discrete, timed and continuous behaviors. In: Pillars of Computer Science, pp. 475–505 (2008)
Pike, R.: The text editor sam. Software: Practice and Experience 17(11), 813–845 (1987)
Spear, C.: SystemVerilog for Verification. Springer (2006)
Stephen, G.A.: String searching algorithms. World Scientific (1994)
Thompson, K.: Programming techniques: Regular expression search algorithm. Communications of the ACM, 419–422 (1968)
Vijayaraghavan, S., Ramanathan, M.: A practical guide for SystemVerilog assertions. Springer (2006)
Weiner, P.: Linear pattern matching algorithms. Switching and Automata Theory (1973)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ulus, D., Ferrère, T., Asarin, E., Maler, O. (2014). Timed Pattern Matching. In: Legay, A., Bozga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2014. Lecture Notes in Computer Science, vol 8711. Springer, Cham. https://doi.org/10.1007/978-3-319-10512-3_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-10512-3_16
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10511-6
Online ISBN: 978-3-319-10512-3
eBook Packages: Computer ScienceComputer Science (R0)