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Succinctness gap between monadic logic and duration calculus

Rabinovich A.

Fundamenta Informaticae

2000

Vol. 42, Nr 2

201-210

In [8, 11] the expressive completeness of the Propositional fragment of Duration Calculus relative to monadic first-order logic of order was established. In this paper we show that there is at least an exponential blow-up in every meaning preserving translation from monadic logic to PDC. Hence, there exists an exponential gap between the succinctness of monadic logic and that of duration calculus.

Truth of duration calculus formulae in timed frames

Middelburg K.A.

Fundamenta Informaticae

1998

Vol. 36, nr 2,3

235-263

Duration calculus is a logical formalism designed for expressing and refining real-time requirements for systems. Timed frames are essentially transition systems meant for modeling the time-dependent behaviour of programs. We investigate the interpretation of duration calculus formulae in timed frames. We elaborate this topic from different angles and show that they agree with each other. The resulting interpretation is expected to make it generally easier to establish semantic links between duration calculus and formalisms aimed at programming. Such semantic links are prerequisites for a solid underpinning of approaches to system development that cover requirement capture through coding using both duration calculus and some formalism(s) at programming.