## Chatterjee, Krishnendu and Henzinger, Monika and Loitzenbauer, Veronika - Improved Algorithms for Parity and Streett objectives

lmcs:3953 - Logical Methods in Computer Science, September 26, 2017, Volume 13, Issue 3
Improved Algorithms for Parity and Streett objectives

Authors: Chatterjee, Krishnendu and Henzinger, Monika and Loitzenbauer, Veronika

The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on $n$ vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time $O(n^{5/2})$ and for (2) k-pair Streett objectives in graphs in time $O(n^2 + nk \log n)$. For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years.

Source : oai:arXiv.org:1410.0833
DOI : 10.23638/LMCS-13(3:26)2017
Volume: Volume 13, Issue 3
Published on: September 26, 2017
Submitted on: September 26, 2017
Keywords: Computer Science - Data Structures and Algorithms,Computer Science - Logic in Computer Science,F.2.2,F.3.1