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Automatabased verification of linear temporal logic models with bounded variability
 In TIME
, 2012
"... Abstract—A model has variability bounded by v/k when the state changes at most v times over any linear interval containing k time instants. When interpreted over models with bounded variability, specification formulae that contain redundant metric information—through the usage of next operators—can ..."
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Abstract—A model has variability bounded by v/k when the state changes at most v times over any linear interval containing k time instants. When interpreted over models with bounded variability, specification formulae that contain redundant metric information—through the usage of next operators—can be simplified without affecting their validity. This paper shows how to harness this simplification in practice: we present a translation of LTL into Büchi automata that removes redundant metric information, hence makes for more efficient verification over models with bounded variability. To show the feasibility of the approach, we also implement a proofofconcept translation in ProMeLa and verify it using the Spin offtheshelf model checker. I. INTRODUCTION AND OVERVIEW Linear temporal logic (LTL) formulae model linear se
Bounded Variability of Metric Temporal Logic
, 2013
"... Previous work has shown that reasoning with realtime temporal logics is often simpler when restricted to models with bounded variability—where no more than v events may occur every V time units, for given v, V. When reasoning about formulas with intrinsic bounded variability, one can employ the sim ..."
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Previous work has shown that reasoning with realtime temporal logics is often simpler when restricted to models with bounded variability—where no more than v events may occur every V time units, for given v, V. When reasoning about formulas with intrinsic bounded variability, one can employ the simpler techniques that rely on bounded variability, without any loss of generality. What is then the complexity of algorithmically deciding which formulas have intrinsic bounded variability? In this paper, we study the problem with reference to Metric Temporal Logic (MTL). We prove that deciding bounded variability of MTL formulas is undecidable over densetime models, but with a undecidability degree lower than generic densetime MTL satisfiability. Over discretetime models, instead, deciding MTL bounded variability has the same exponentialspace complexity as satisfiability. To complement these negative results, we also discuss fragments of MTL that are more amenable to reasoning about bounded variability, again both for discrete and for densetime models. 1 The Benefits of Bounding Variability In yet another instance of the principle that “there ain’t no such thing as a free lunch”, expressiveness of formal languages comes with a significant cost to pay in terms of complexity—and possibly undecidability—of algorithmic analysis. The tradeoff between expressiveness and complexity is particularly critical for the realtime temporal logics, which dwell on the border of intractability. A chief research challenge is, therefore, identifying expressive temporal logic fragments without letting the “dark side ” of undecidability [6] prevail and abate practical usability.