# Quasipolynomial set-based symbolic algorithms for parity games

Chatterjee K, Dvořák W, Henzinger MH, Svozil A. 2018. Quasipolynomial set-based symbolic algorithms for parity games. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning, EPiC Series in Computing, vol. 57, 233–253.

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Author
Chatterjee, KrishnenduISTA ; Dvořák, Wolfgang; Henzinger, MonikaISTA ; Svozil, Alexander
Department
Series Title
EPiC Series in Computing
Abstract
Solving parity games, which are equivalent to modal μ-calculus model checking, is a central algorithmic problem in formal methods, with applications in reactive synthesis, program repair, verification of branching-time properties, etc. Besides the standard compu- tation model with the explicit representation of games, another important theoretical model of computation is that of set-based symbolic algorithms. Set-based symbolic algorithms use basic set operations and one-step predecessor operations on the implicit description of games, rather than the explicit representation. The significance of symbolic algorithms is that they provide scalable algorithms for large finite-state systems, as well as for infinite-state systems with finite quotient. Consider parity games on graphs with n vertices and parity conditions with d priorities. While there is a rich literature of explicit algorithms for parity games, the main results for set-based symbolic algorithms are as follows: (a) the basic algorithm that requires O(nd) symbolic operations and O(d) symbolic space; and (b) an improved algorithm that requires O(nd/3+1) symbolic operations and O(n) symbolic space. In this work, our contributions are as follows: (1) We present a black-box set-based symbolic algorithm based on the explicit progress measure algorithm. Two important consequences of our algorithm are as follows: (a) a set-based symbolic algorithm for parity games that requires quasi-polynomially many symbolic operations and O(n) symbolic space; and (b) any future improvement in progress measure based explicit algorithms immediately imply an efficiency improvement in our set-based symbolic algorithm for parity games. (2) We present a set-based symbolic algorithm that requires quasi-polynomially many symbolic operations and O(d · log n) symbolic space. Moreover, for the important special case of d ≤ log n, our algorithm requires only polynomially many symbolic operations and poly-logarithmic symbolic space.
Publishing Year
Date Published
2018-10-23
Proceedings Title
22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning
Acknowledgement
A. S. is fully supported by the Vienna Science and Technology Fund (WWTF) through project ICT15-003. K.C. is supported by the Austrian Science Fund (FWF) NFN Grant No S11407-N23 (RiSE/SHiNE) and an ERC Starting grant (279307: Graph Games). For M.H the research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) /ERC Grant Agreement no. 340506.
Volume
57
Page
233-253
Conference
LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning
Conference Location
Awassa, Ethiopia
Conference Date
2018-11-17 – 2018-11-21
ISSN
IST-REx-ID

### Cite this

Chatterjee K, Dvořák W, Henzinger MH, Svozil A. Quasipolynomial set-based symbolic algorithms for parity games. In: 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. Vol 57. EasyChair; 2018:233-253. doi:10.29007/5z5k
Chatterjee, K., Dvořák, W., Henzinger, M. H., & Svozil, A. (2018). Quasipolynomial set-based symbolic algorithms for parity games. In 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning (Vol. 57, pp. 233–253). Awassa, Ethiopia: EasyChair. https://doi.org/10.29007/5z5k
Chatterjee, Krishnendu, Wolfgang Dvořák, Monika H Henzinger, and Alexander Svozil. “Quasipolynomial Set-Based Symbolic Algorithms for Parity Games.” In 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, 57:233–53. EasyChair, 2018. https://doi.org/10.29007/5z5k.
K. Chatterjee, W. Dvořák, M. H. Henzinger, and A. Svozil, “Quasipolynomial set-based symbolic algorithms for parity games,” in 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Awassa, Ethiopia, 2018, vol. 57, pp. 233–253.
Chatterjee K, Dvořák W, Henzinger MH, Svozil A. 2018. Quasipolynomial set-based symbolic algorithms for parity games. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning. LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning, EPiC Series in Computing, vol. 57, 233–253.
Chatterjee, Krishnendu, et al. “Quasipolynomial Set-Based Symbolic Algorithms for Parity Games.” 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol. 57, EasyChair, 2018, pp. 233–53, doi:10.29007/5z5k.
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