A Recursive Approach to Solving Parity Games in Quasipolynomial Time

Lehtinen, Karoliina; Parys, Paweł; Schewe, Sven; Wojtczak, Dominik

doi:10.46298/lmcs-18(1:8)2022

Cited by 11 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This problem is still intensely studied due to its broad applications. It also is one of the few problems which canonically lie in NP ∩ coNP (even in UP ∩ coUP [19]), with recent breakthroughs achieving quasi-polynomial algorithms [4,14,28].…”

Section: Synthesis and Gamesmentioning

confidence: 99%

Guessing Winning Policies in LTL Synthesis by Semantic Learning

Křetínský

Meggendorfer

Prokop

et al. 2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We provide a learning-based technique for guessing a winning strategy in a parity game originating from an LTL synthesis problem. A cheaply obtained guess can be useful in several applications. Not only can the guessed strategy be applied as best-effort in cases where the game’s huge size prohibits rigorous approaches, but it can also increase the scalability of rigorous LTL synthesis in several ways. Firstly, checking whether a guessed strategy is winning is easier than constructing one. Secondly, even if the guess is wrong in some places, it can be fixed by strategy iteration faster than constructing one from scratch. Thirdly, the guess can be used in on-the-fly approaches to prioritize exploration in the most fruitful directions.In contrast to previous works, we (i) reflect the highly structured logical information in game’s states, the so-called semantic labelling, coming from the recent LTL-to-automata translations, and (ii) learn to reflect it properly by learning from previously solved games, bringing the solving process closer to human-like reasoning.

show abstract

Section: Synthesis and Gamesmentioning

confidence: 99%

Guessing Winning Policies in LTL Synthesis by Semantic Learning

Křetínský

Meggendorfer

Prokop

et al. 2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…More recently, a quasi-polynomial version was devised by Parys [32] through an ingenious pruning of the recursion tree. This was later refined by Lehtinen et al [30], who observed that the tree of recursive calls follows a particular construction of universal trees. Subsequently, Jurdziński and Morvan [26] generalized it to a generic algorithm parameterized by a universal tree.…”

Section: Introductionmentioning

confidence: 97%

Beyond Value Iteration for Parity Games: Strategy Iteration with Universal Trees

Koh¹,

Loho²

2021

Preprint

View full text Add to dashboard Cite

Parity games have witnessed several new quasi-polynomial algorithms since the breakthrough result of Calude et al. (2017). The central combinatorial object underlying these approaches is a universal tree, as identified by Czerwiński et al. (2019). By providing a quasi-polynomial lower bound on the size of universal trees, they have highlighted a barrier that must be overcome by all existing approaches to attain polynomial runtime. This is due to the existence of worst case instances which force these algorithms to explore a large portion of the tree.As an attempt to overcome this barrier, we propose a strategy iteration framework which can be applied on any universal tree. It is at least as fast as its value iteration counterparts, while allowing one to take bigger leaps in the universal tree. Value iteration -asymptotically the fastest known algorithm for parity games -is a repeated application of operators associated with arcs in the game graph to obtain the least fixed point. Our main technical contribution is an efficient method for computing the least fixed point of operators associated with arcs in a strategy subgraph. This is achieved via a careful adaptation of shortest path algorithms to the setting of ordered trees. By plugging in the universal tree of Jurdziński and Lazić (2017), or the Strahler universal tree of Daviaud et al. (2020), we obtain instantiations of the general framework that take time O(mn 2 log n log d) and O(mn 2 log 3 n log d) respectively per iteration.

show abstract

“…Most research has focused on parity games: as the most special class of games, algorithms have the option to use the special structure of their problems, and they are most directly linked to the synthesis and verification problems mentioned earlier. Parity games have thus enjoyed a special status among graph games and the quest for efficient algorithms [13,11,26,38,7,37,27,4,3] for solving them has been an active field of research during the last decades, which has received further boost with the arrival of quasi-polynomial techniques [8,18,15,23,24,10].…”

Section: Introductionmentioning

confidence: 99%

An Objective Improvement Approach to Solving Discounted Payoff Games

Dell'Erba,

Dumas,

Schewe

2023

Electron. Proc. Theor. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the constraints that optimal solutions need to satisfy, and devised a novel way to converge to them, which is entirely symmetric. It also challenges the gospel that methods for solving payoff games are either based on strategy improvement or on value iteration.

show abstract

A Recursive Approach to Solving Parity Games in Quasipolynomial Time

Cited by 11 publications

References 20 publications

Guessing Winning Policies in LTL Synthesis by Semantic Learning

Guessing Winning Policies in LTL Synthesis by Semantic Learning

Beyond Value Iteration for Parity Games: Strategy Iteration with Universal Trees

An Objective Improvement Approach to Solving Discounted Payoff Games

Contact Info

Product

Resources

About