Reasoning About Transfinite Sequences

  • Stéphane Demri
  • David Nowak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3707)


We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on ω-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on ω k -sequences is expspace-complete when the integers are represented in binary, and pspace-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Stéphane Demri
    • 1
  • David Nowak
    • 2
  1. 1.LSV/CNRS UMR 8643 & INRIA Futurs projet SECSI & ENS CachanFrance
  2. 2.Department of Information ScienceThe University of TokyoJapan

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