Characteristic Formulae for Timed Automata

Abstract

This paper offers characteristic formula constructions in the real-
time logic L for several behavioural relations between (states of)
timed automata. The behavioural relations studied in this work are
timed (bi)similarity, timed ready simulation, faster-than bisimilarity
and timed trace inclusion. The characteristic formulae delivered by
our constructions have size which is linear in that of the timed
automaton they logically describe. This also applies to the characteristic
formula for timed bisimulation equivalence, for which an exponential
space construction was previously offered by Laroussinie, Larsen and
Weise.