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Near-Linear Time Algorithms for Streett Objectives in Graphs and MDPs

Authors Krishnendu Chatterjee, Wolfgang Dvořák, Monika Henzinger, Alexander Svozil

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Krishnendu Chatterjee
  • IST Austria, Klosterneuburg, Austria
Wolfgang Dvořák
  • Institute of Logic and Computation, TU Wien, Austria
Monika Henzinger
  • Theory and Application of Algorithms, University of Vienna, Austria
Alexander Svozil
  • Theory and Application of Algorithms, University of Vienna, Austria

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Krishnendu Chatterjee, Wolfgang Dvořák, Monika Henzinger, and Alexander Svozil. Near-Linear Time Algorithms for Streett Objectives in Graphs and MDPs. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


The fundamental model-checking problem, given as input a model and a specification, asks for the algorithmic verification of whether the model satisfies the specification. Two classical models for reactive systems are graphs and Markov decision processes (MDPs). A basic specification formalism in the verification of reactive systems is the strong fairness (aka Streett) objective, where given different types of requests and corresponding grants, the requirement is that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All omega-regular objectives can be expressed as Streett objectives and hence they are canonical in verification. Consider graphs/MDPs with n vertices, m edges, and a Streett objectives with k pairs, and let b denote the size of the description of the Streett objective for the sets of requests and grants. The current best-known algorithm for the problem requires time O(min(n^2, m sqrt{m log n}) + b log n). In this work we present randomized near-linear time algorithms, with expected running time O~(m + b), where the O~ notation hides poly-log factors. Our randomized algorithms are near-linear in the size of the input, and hence optimal up to poly-log factors.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
  • Software and its engineering → Formal software verification
  • model checking
  • graph games
  • Streett games


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