A decidable recursive logic forweighted transition systems

Kim Guldstrand Larsen, Radu Mardare, Bingtian Xue

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

2 Citations (Scopus)


In this paper we develop and study the Recursive Weighted Logic (RWL), a multi-modal logic that expresses qualitative and quantitative properties of labelled weighted transition systems (LWSs). LWSs are transition systems labelled with actions and real-valued quantities representing the costs of transitions with respect to various resources. RWL uses first-order variables to measure local costs. The main syntactic operators are similar to the ones of timed logics for real-time systems. In addition, our logic is endowed, with simultaneous recursive equations, which specify the weakest properties satisfied by the recursive variables. We prove that unlike in the case of the timed logics, the satisfiability problem for RWL is decidable. The proof uses a variant of the region construction technique used in literature with timed automata, which we adapt to the specific settings of RWL. This paper extends previous results that we have demonstrated for a similar but much more restrictive logic that can only use one variable for each type of resource to encode logical properties.

Original languageEnglish
Title of host publicationTheoretical Aspects of Computing – ICTAC 2014
Subtitle of host publicationProceedings of 11th International Colloquium Bucharest, Romania, September 17-19, 2014
EditorsGabriel Ciobanu, Dominique Méry
Place of PublicationCham
Number of pages17
ISBN (Print)9783319108810, 9783319108827
Publication statusPublished - 23 Sep 2014

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
ISSN (Print)0302-9743


  • labelled weighted transition system
  • maximal fixed point computation
  • multi-modal logic


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