# Symmetric Strategy Improvement

@inproceedings{Schewe2015SymmetricSI, title={Symmetric Strategy Improvement}, author={Sven Schewe and Ashutosh Trivedi and Thomas Varghese}, booktitle={ICALP}, year={2015} }

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of…

## 16 Citations

A Delayed Promotion Policy for Parity Games

- Mathematics, Computer ScienceGandALF
- 2016

A new instantiation, called delayed promotion, is proposed that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case, and not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.

A delayed promotion policy for parity games

- Computer Science, MathematicsInf. Comput.
- 2018

A new instantiation, called delayed promotion, is proposed that tries to reduce the possible exponential behaviors exhibited by the original method in the worst case, and often outperforms both the state-of-the-art solvers and the original priority promotion approach.

Improving Priority Promotion for Parity Games

- Computer ScienceHaifa Verification Conference
- 2016

A new instantiation, called region recovery, is proposed that tries to reduce the possible exponential behaviours exhibited by the original method in the worst case, and not only often outperforms the original priority promotion approach, but so far no exponential worst case is known.

Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games

- Computer Science, MathematicsVMCAI
- 2017

This work presents a method that - in contrast to existing techniques - tackles both aspects with the best suited approach and works exclusively on the 2.5 player game itself, powerful enough to handle games with several million states.

Improvement in Small Progress Measures

- Mathematics, Computer ScienceGandALF
- 2015

The algorithm is modified so that it derives the winning strategy for both players in one pass, which reduces the upper bound on strategy derivation for SPM to O(dm.(n/floor(d/2))^floor( d/2)).

Parity Games with Weights

- Mathematics, Computer ScienceCSL
- 2018

This work investigates the problem of determining, for a given threshold b, whether the protagonist has a strategy of quality at most b and shows this problem to be EXPTIME-complete and presents tight bounds on the quality of winning strategies for the protagonist.

Parity Games with Weights

- Mathematics, Computer ScienceLog. Methods Comput. Sci.
- 2019

It is shown that solving parity games with costs with arbitrary integer weights is in NP $\cap$ coNP, the signature complexity for games of this type, and that the protagonist has finite-state winning strategies, and tight pseudo-polynomial bounds for the memory he needs to win the game are presented.

An ordered approach to solving parity games in quasi polynomial time and quasi linear space

- Mathematics, Computer ScienceSPIN
- 2017

A first implementation for a quasi-polynomial algorithm is provided, and a number of side results are provided, including minor algorithmic improvements, a quasi bi-linear complexity in the number of states and edges for a fixed number of colours, and matching lower bounds for the algorithm of Calude et al.

An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2019

This work provides a first implementation for a quasi-polynomial algorithm, test it on small examples, and provides a number of side results, including minor algorithmic improvements, and a complexity index associated to the approach, which is compared to the recently proposed register index.

06 16 8 v 1 [ cs . G T ] 1 7 A pr 2 01 8 Parity Games with Weights

- 2018

Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and…

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