Model checking discounted temporal properties Journal Article


Author(s): de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A; Majumdar, Ritankar S; Stoelinga, Mariëlle
Article Title: Model checking discounted temporal properties
Affiliation
Abstract: Temporal logic is two-valued: formulas are interpreted as either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a generalization of the branching-time logic CTL which achieves robustness with respect to model perturbations by giving a quantitative interpretation to predicates and logical operators, and by discounting the importance of events according to how late they occur. In every state, the value of a formula is a real number in the interval [0,1], where 1 corresponds to truth and 0 to falsehood. The boolean operators and and or are replaced by min and max, the path quantifiers ∃ and ∀ determine sup and inf over all paths from a given state, and the temporal operators ⋄ and □ specify sup and inf over a given path; a new operator averages all values along a path. Furthermore, all path operators are discounted by a parameter that can be chosen to give more weight to states that are closer to the beginning of the path. We interpret the resulting logic DCTL over transition systems, Markov chains, and Markov decision processes. We present two semantics for DCTL: a path semantics, inspired by the standard interpretation of state and path formulas in CTL, and a fixpoint semantics, inspired by the μ-calculus evaluation of CTL formulas. We show that, while these semantics coincide for CTL, they differ for DCTL, and we provide model-checking algorithms for both semantics.
Keywords: model checking; logic; quantitative systems; discounting; CTL
Journal Title: Theoretical Computer Science
Volume: 345
Issue 1
ISSN: 0304-3975
Publisher: Elsevier  
Date Published: 2005-11-21
Start Page: 139
End Page: 170
DOI: 10.1016/j.tcs.2005.07.033
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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