Logics for real time: Decidability and complexity

Yoram Hirshfeld, Alexander Rabinovich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

77 Scopus citations


Over the last fifteen years formalisms for reasoning about metric properties of computations were suggested and discussed. First as extensions of temporal logic, ignoring the framework of classical predicate logic, and then, with the authors' work, within the framework of monadic logic of order. Here we survey our work on metric logic comparing it to the previous work in the field. We define a quantitative temporal logic that is based on a simple modality within the framework of monadic predicate Logic. Its canonical model is the real line (and not an ω-sequence of some type). It can be interpreted either by behaviors with finite variability or by unrestricted behaviors. For finite variability models it is as expressive as any logic suggested in the literature. For unrestricted behaviors our treatment is new. In both cases we prove decidability and complexity bounds using general theorems from logic (and not from automata theory).

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalFundamenta Informaticae
Issue number1
StatePublished - Aug 2004


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