# Delay Games with WMSO+U Winning Conditions

@article{Zimmermann2016DelayGW, title={Delay Games with WMSO+U Winning Conditions}, author={Martin Zimmermann}, journal={RAIRO Theor. Informatics Appl.}, year={2016}, volume={50}, pages={145-165} }

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding quantifier, which is able to express (un)boundedness properties.

## 13 Citations

### Unbounded Lookahead in WMSO+U Games

- PhilosophyArXiv
- 2015

This work considers WMSO+U delay games with unbounded lookahead and shows that the winner is always the same, as long as the initial lookahead is large enough and the lookahead tends to infinity.

### Prompt Delay

- Computer ScienceFSTTCS
- 2016

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. Recently, such games with quantitative winning conditions…

### Finite-state Strategies in Delay Games

- Computer ScienceGandALF
- 2017

This work presents a very general framework for computing finite-state strategies in delay games: they exist for all winning conditions that are recognized by automata with acceptance conditions that satisfy a certain aggregation property.

### Finite-state Strategies in Delay Games (full version)

- Computer Science, Mathematics
- 2017

This work presents a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite- state strategy.

### How Much Lookahead is Needed to Win Infinite Games?

- Computer ScienceLog. Methods Comput. Sci.
- 2016

Solving delay games with reachability conditions is shown to be PSPACE-complete by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead and showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead.

### What are Strategies in Delay Games? Borel Determinacy for Games with Lookahead

- Computer ScienceCSL
- 2015

Determinacy of delay games with Borel winning conditions, infinite-duration two-player games in which one player may delay her moves to obtain a lookahead on her opponent's moves, is proved and different notions of universal strategies for both players are introduced.

### Games with costs and delays

- Economics2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2017

The benefit of introducing lookahead is twofold: not only does it allow the delaying player to win games she would lose without, but lookahead also allows her to improve the quality of her winning strategies in games she wins even without lookahead.

### Two-Player Boundedness Counter Games

- Computer Science
- 2022

This work considers two-player zero-sum games with winning objectives beyond regular languages, expressed as a parity condition in conjunction with a Boolean combination of boundedness conditions on a finite set of counters, and proves that they are in solvable in NP ∩ CoNP and in PTime if the parity condition is fixed.

### Security-Aware Synthesis Using Delayed-Action Games

- Computer ScienceCAV
- 2019

A delayed-action games (DAGs) formalism that simulates hidden-information games (HIGs) as SMGs, where hidden information is captured by delaying a player's actions, and proposes a DAG-based framework for strategy synthesis and analysis.

### Stated in terms of uniformization , Hosch and Landweber proved decidability of the uniformization problem for ω-regular relations by Lipschitz-continuous functions and

- Mathematics
- 2017

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. For ω-regular winning conditions it is known that such…

## References

SHOWING 1-10 OF 48 REFERENCES

### Degrees of Lookahead in Context-free Infinite Games

- Computer ScienceCSL
- 2011

The investigation of delay games, infinite games in which one player may postpone her moves for some time to obtain a lookahead on her opponent's moves, shows that the problem of determining the winner is undecidable for deterministic context-free winning conditions.

### Prompt Delay

- Computer ScienceFSTTCS
- 2016

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. Recently, such games with quantitative winning conditions…

### How Much Lookahead is Needed to Win Infinite Games?

- Computer ScienceLog. Methods Comput. Sci.
- 2016

Solving delay games with reachability conditions is shown to be PSPACE-complete by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead and showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead.

### What are Strategies in Delay Games? Borel Determinacy for Games with Lookahead

- Computer ScienceCSL
- 2015

Determinacy of delay games with Borel winning conditions, infinite-duration two-player games in which one player may delay her moves to obtain a lookahead on her opponent's moves, is proved and different notions of universal strategies for both players are introduced.

### Optimal Bounds in Parametric LTL Games

- Computer ScienceGandALF
- 2011

This work presents an algorithm to determine optimal variable valuations that allow a player to win a game and shows how to determine whether a player wins a game with respect to some, infinitely many, or all valuations.

### Parity and Streett Games with Costs

- EconomicsLog. Methods Comput. Sci.
- 2014

Two winning conditions are introduced, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses, which generalize the corresponding classical omega-regular conditions and the corresponding finitary conditions.

### Degrees of Lookahead in Regular Infinite Games

- MathematicsLog. Methods Comput. Sci.
- 2010

It is shown that for regular infinite games the solvability by continuous strategies is decidable, and that a continuous strategy can always be reduced to one of bounded lookahead.

### Infinite Games and Uniformization

- MathematicsICLA
- 2011

The problem of solvability of infinite games is closely connected with the classical question of uniformization of relations by functions of a given class and recent results on infinite games that are motivated by the uniformization problem are discussed.

### Weak MSO+U with Path Quantifiers over Infinite Trees

- Mathematics, Computer ScienceICALP
- 2014

This paper shows that over infinite trees, satisfiability is decidable for weak monadic second-order logic extended by the unbounding quantifier \(\mathsf U\) and quantification over infinite paths.…

### Solving sequential conditions by finite-state strategies

- Mathematics
- 1969

Our main purpose is to present an algorithm which decides whether or not a condition 𝕮(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This…