## Abstract

Real-time systems operate in “real,” continuous time and state changes may occur at any real-numbered time point. Yet many verification methods are based on the assumption that states are observed at integer time points only. What can we conclude if a real-time system has been shown “correct” for integral observations?

Integer time verification techniques suffice if the problem of whether all real-numbered behaviors of a system satisfy a property can be reduced to the question of whether the integral observations satisfy a (possibly modified) property. We show that this reduction is possible for a large and important class of systems and properties: the class of systems includes all systems that can be modeled as timed transition systems; the class of properties includes time-bounded invariance and time-bounded response.

A full version of this paper (including all proofs) is available as a technical report from Cornell University and Stanford University. The research was supported in part by the National Science Foundation under grants CCR-89-11512 and CCR-89-13641, by the Defense Advanced Research Projects Agency under contract NAG2-703, by the United States Air Force Office of Scientific Research under contract AFOSR-90-0057, and by the European Community ESPRIT Basic Research Action Project 3096 (SPEC).

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Henzinger, T.A., Manna, Z., Pnueli, A. (1992). What good are digital clocks?. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_103

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