10.4230/LIPICS.CONCUR.2019.7
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Dvorák, Wolfgang
Wolfgang
Dvorák
Henzinger, Monika
Monika
Henzinger
Svozil, Alexander
Alexander
Svozil
Near-linear time algorithms for Streett objectives in graphs and MDPs
LIPIcs
Schloss Dagstuhl - Leibniz-Zentrum für Informatik
2019
2019-09-18T08:07:58Z
2020-01-21T13:21:51Z
conference
https://research-explorer.app.ist.ac.at/record/6887
https://research-explorer.app.ist.ac.at/record/6887.json
730112 bytes
application/pdf
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.