Flatness Is Not a Weakness

  • Hubert Comon
  • Vèronique Cortier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1862)


We propose an extension, called \( \mathcal{L}_p^ + , o \), of the temporal logic LTL, which enables talking about finitely many register values: the models are infinite words over tuples of integers (resp. real numbers). The formulas of \( \mathcal{L}_p^ + , o \) are flat: on the left of an until, only atomic formulas or LTL formulas are allowed. We prove, in the spirit of the correspondence between automata and temporal logics, that the models of a \( \mathcal{L}_p^ + , o \) formula are recognized by a piecewise flat counter machine; for each state q, at most one loop of the machine on q may modify the register values.

Emptiness of (piecewise). at counter machines is decidable (this follows from a result in [9]). It follows that satisfiability and model-checking the negation of a formula are decidable for \( \mathcal{L}_p^ + , o \). On the other hand, we show that inclusion is undecidable for such languages. This shows that validity and model-checking positive formulas are undecidable.


Counter automata temporal logics model-checking verification logic in computer science 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hubert Comon
    • 1
  • Vèronique Cortier
    • 1
  1. 1.LSV, Ecole Normale Supèrieure de CachanCachan cedexFrance

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