Conditionally optimal algorithms for generalized Büchi Games

K. Chatterjee, W. Dvorák, M. Henzinger, V. Loitzenbauer, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016.

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Conference Paper | Published | English
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Series Title
LIPIcs
Abstract
Games on graphs provide the appropriate framework to study several central problems in computer science, such as verification and synthesis of reactive systems. One of the most basic objectives for games on graphs is the liveness (or Büchi) objective that given a target set of vertices requires that some vertex in the target set is visited infinitely often. We study generalized Büchi objectives (i.e., conjunction of liveness objectives), and implications between two generalized Büchi objectives (known as GR(1) objectives), that arise in numerous applications in computer-aided verification. We present improved algorithms and conditional super-linear lower bounds based on widely believed assumptions about the complexity of (A1) combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph games with n vertices, m edges, and generalized Büchi objectives with k conjunctions. First, we present an algorithm with running time O(k*n^2), improving the previously known O(k*n*m) and O(k^2*n^2) worst-case bounds. Our algorithm is optimal for dense graphs under (A1). Second, we show that the basic algorithm for the problem is optimal for sparse graphs when the target sets have constant size under (A2). Finally, we consider GR(1) objectives, with k_1 conjunctions in the antecedent and k_2 conjunctions in the consequent, and present an O(k_1 k_2 n^{2.5})-time algorithm, improving the previously known O(k_1*k_2*n*m)-time algorithm for m > n^{1.5}.
Publishing Year
Date Published
2016-08-01
Acknowledgement
K. C., M. H., and W. D. are partially supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-003. K. C. is partially supported by the Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE) and an ERC Start grant (279307
Volume
58
Article Number
25
Conference
MFCS: Mathematical Foundations of Computer Science (SG)
Conference Location
Krakow, Poland
Conference Date
2016-08-22 – 2016-08-26
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Chatterjee K, Dvorák W, Henzinger M, Loitzenbauer V. Conditionally optimal algorithms for generalized Büchi Games. In: Vol 58. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2016. doi:10.4230/LIPIcs.MFCS.2016.25
Chatterjee, K., Dvorák, W., Henzinger, M., & Loitzenbauer, V. (2016). Conditionally optimal algorithms for generalized Büchi Games (Vol. 58). Presented at the MFCS: Mathematical Foundations of Computer Science (SG), Krakow, Poland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2016.25
Chatterjee, Krishnendu, Wolfgang Dvorák, Monika Henzinger, and Veronika Loitzenbauer. “Conditionally Optimal Algorithms for Generalized Büchi Games,” Vol. 58. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. https://doi.org/10.4230/LIPIcs.MFCS.2016.25.
K. Chatterjee, W. Dvorák, M. Henzinger, and V. Loitzenbauer, “Conditionally optimal algorithms for generalized Büchi Games,” presented at the MFCS: Mathematical Foundations of Computer Science (SG), Krakow, Poland, 2016, vol. 58.
Chatterjee K, Dvorák W, Henzinger M, Loitzenbauer V. 2016. Conditionally optimal algorithms for generalized Büchi Games. MFCS: Mathematical Foundations of Computer Science (SG), LIPIcs, vol. 58.
Chatterjee, Krishnendu, et al. Conditionally Optimal Algorithms for Generalized Büchi Games. Vol. 58, 25, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016, doi:10.4230/LIPIcs.MFCS.2016.25.
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