On Expressive Completeness of Duration and Mean Value Calculi (Extended Abstract)

Alexander Rabinovich
1997 Electronical Notes in Theoretical Computer Science  
This paper compares the expressive power of rst-order monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of two formalisms for the speci cation 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 rst-order logic of order. A new semantics for the chop operator used in these real-time formalisms is also
more » ... d, and the expressive completeness results achieved in the paper indicate that the new de nition might be more natural than the original one. We provide a characterization of the expressive p o wer 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 rst-order logic of order.
doi:10.1016/s1571-0661(05)80476-1 fatcat:imuhell3zjatbjiuj5yfh5qmje