On expressive completeness of duration and mean value calculi (extended abstract)

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Abstract

This paper compares the expressive power of first-order monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of two formalisms for the specification of real-time systems, the propositional versions of duration and mean value calculi. Our results show that the propositional mean value calculus is expressively complete for monadic first-order logic of order. A new semantics for the chop operator used in these real-time formalisms is also proposed, and the expressive completeness results achieved in the paper indicate that the new definition might be more natural than the original one. We provide a characterization of the expressive power of the propositional duration calculus and investigate the connections between the propositional duration calculus and star-free regular expressions. Finally, we show that there exists at least an exponential gap between the succinctness of the propositional duration (mean value) calculus and that of monadic first-order logic of order.

Original languageEnglish
Pages (from-to)248-261
Number of pages14
JournalElectronic Notes in Theoretical Computer Science
Volume7
DOIs
StatePublished - 1997
EventEXPRESS '97 - Santa Margherita Ligure, Italy
Duration: 8 Sep 199712 Sep 1997

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