From Propositional to First-Order Monitoring

  • Andreas Bauer
  • Jan-Christoph Küster
  • Gil Vegliach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8174)


The main purpose of this paper is to introduce a first-order temporal logic, LTLFO, and a corresponding monitor construction based on a new type of automaton, called spawning automaton.

Specifically, we show that monitoring a specification in LTLFO boils down to an undecidable decision problem. The proof of this result revolves around specific ideas on what we consider a “proper” monitor. As these ideas are general, we outline them first in the setting of standard LTL, before lifting them to the setting of first-order logic and LTLFO. Although due to the above result one cannot hope to obtain a complete monitor for LTLFO, we prove the soundness of our automata-based construction and give experimental results from an implementation. These seem to substantiate our hypothesis that the automata-based construction leads to efficient runtime monitors whose size does not grow with increasing trace lengths (as is often observed in similar approaches). However, we also discuss formulae for which growth is unavoidable, irrespective of the chosen monitoring approach.


Model Check Temporal Logic Word Problem Function Symbol Kripke Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andreas Bauer
    • 1
    • 2
  • Jan-Christoph Küster
    • 1
    • 2
  • Gil Vegliach
    • 1
  1. 1.NICTA Software Systems Research GroupAustralia
  2. 2.Australian National UniversityAustralia

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