The Expressive Power of Clocks

Abstract

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 Buchi, 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.