# The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs

@article{Canavoi2014TheDS, title={The discrete strategy improvement algorithm for parity games and complexity measures for directed graphs}, author={Felix Canavoi and Erich Gr{\"a}del and Roman Rabinovich}, journal={Theor. Comput. Sci.}, year={2014}, volume={560}, pages={235-250} }

Abstract The problem whether winning regions and wining strategies for parity games can be computed in polynomial time is a major open problem in the field of infinite games, which is relevant for many applications in logic and formal verification. For some time the discrete strategy improvement algorithm due to Jurdzinski and Voge had been considered to be a candidate for solving parity games in polynomial time. However, it has recently been proved by Oliver Friedmann that this algorithm…

## 3 Citations

### Deciding parity games in quasipolynomial time

- Computer Science, MathematicsSTOC
- 2017

It is shown that the parity game can be solved in quasipolynomial time and it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n), for any c, unless FPT = W[1].

### Synthesis of winning strategies for interaction under partial information

- Computer Science, Mathematics
- 2013

This work adresses the strategy problem for multiplayer games with imperfect information which are of infinite duration and have (up to) contextfree winning conditions and provides a complete characterization of all communication graphs for which synthesis is decidable for locally decomposable regular and contextfree specifications.

### Advanced reduction techniques for model checking

- Computer Science
- 2013

This paper presents a treatment of the construction of a Boolean equation system using a model derived from the explicit specification of a μ-calculus formula.

## References

SHOWING 1-10 OF 25 REFERENCES

### A Discrete Strategy Improvement Algorithm for Solving Parity Games

- Computer ScienceCAV
- 2000

A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus.…

### Small Progress Measures for Solving Parity Games

- Computer ScienceSTACS
- 2000

A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.

### Clique-Width and Parity Games

- Computer Science, MathematicsCSL
- 2007

This work presents a polynomial-time algorithm for parity games on graphs of bounded clique-width (class of graphs containing e.g. complete bipartite graphs and cliques), thus completing the picture of the exact complexity of solving parity games.

### Graph complexity measures and monotonicity

- Mathematics
- 2013

A weak variant of monotonicity is proved for two cops, a property of winning cop strategies, which implies the existence of suitable decompositions of the given graphs which allow for efficient algorithms for difficult computational problems.

### A Subexponential Lower Bound for Zadeh's Pivoting Rule for Solving Linear Programs and Games

- Computer ScienceIPCO
- 2011

The first subexponential lower bound of the form 2Ω(√n) lower bound is obtained by utilizing connections between pivoting steps performed by simplex-based algorithms and improving switches performed by policy iteration algorithms for 1-player and 2-player games.

### Exponential Lower Bounds for Solving Infinitary Payoff Games and Linear Programs

- Computer Science
- 2011

Parity games form an intriguing family of infinitary payoff games whose solution
is equivalent to the solution of important problems in automatic verification and
automata theory. They also form a…

### DRAFT March 20 , 2012 A subexponential lower bound for the Least Recently Considered rule for solving linear programs and games

- Computer Science
- 2012

The first subexponential lower bound for Cunningham’s Least Recently Considered rule, also known as the ROUND-ROBIN rule, is provided by utilizing connections between pivoting steps performed by simplex-based algorithms and improving switches performed by policy iteration algorithms for 1player and 2-player games.

### Digraph measures: Kelly decompositions, games, and orderings

- Mathematics, Computer ScienceSODA '07
- 2007