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The expressive power of clocks


Part of the Lecture Notes in Computer Science book series (LNCS,volume 944)


We investigate the expressive power of timing restrictions on labeled transition systems. In particular, we show how constraints on clock variables together with a uniform liveness condition—the divergence of time—can express Büchi, Muller, Streett, Rabin, and weak and strong fairness conditions on a given labeled transition system. We then consider the effect, on both timed and time-abstract expressiveness, of varying the following parameters: time domain (discrete or dense), number of clocks, number of states, and size of constants used in timing restrictions.


  • Expressive Power
  • Regular Language
  • Finite Automaton
  • Label Transition System
  • Acceptance Condition

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This research was supported in part by the National Science Foundation under grant CCR-9200794, by the United States Air Force Office of Scientific Research under contract F49620-93-1-0056, by the Defense Advanced Research Projects Agency under grant NAG2-892, and by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University, Contract Number DAAL03-91-C-0027.

The full version of this paper is available from the Department of Computer Science, Cornell University, Ithaca, NY 14853, as Technical Report TR95-1496.

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Henzinger, T.A., Kopke, P.W., Wong-Toi, H. (1995). The expressive power of clocks. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg.

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