Rabin games and colourful universal trees

R Majumdar, I Sağlam, KS Thejaswini - … on Tools and Algorithms for the …, 2024 - Springer
Rabin games is a progress measure lifting algorithm where the lifting is performed on succinct,
colourful, universal trees… uses our construction of colourful universal trees. Therefore, we …

[PDF][PDF] Regular Games

N FIJALKOW, F HORN - Games on Graphs, 2023 - arxiv.org
Rabin, Streett, and Muller games. Finally, Section 2.6 is devoted to the combinatorial notion
of the Zielonka tree, … If xp is universal, we construct a new positive valuation as follows. We …

[PDF][PDF] Rabin's Theorem

J Tan - 2019 - math.mcmaster.ca
… of deterministic parity games. Finally we introduce infinite binary trees as well as the … for a
special class of regular languages known as universal Büchi languages and then show that we …

On the size of good-for-games Rabin automata and its link with the memory in Muller games

A Casares, T Colcombet, K Lehtinen - arXiv preprint arXiv:2204.11333, 2022 - arxiv.org
… of colours, called the winning condition (we call Wgames the … games played between the
existential and the universal … We equip trees with an order in order to navigate in them. An …

[PDF][PDF] From Muller to Parity and Rabin Automata: Optimal Transformations Preserving (History) Determinism

T Preserving - antonio-casares.github.io
… We study transformations of automata and games using … of infinite trees represented as a
non-deterministic parity tree-… will always assume that the set of colours is a subset of N and 𝜙 is …

[HTML][HTML] The Rabin index of parity games: Its complexity and approximation

M Huth, JHP Kuo, N Piterman - Information and Computation, 2015 - Elsevier
… be expressed as an alternation of existential and universal quantification. In fact, deciding
the … Our algorithm rabin for computing the Rabin index of a colored arena is shown in Fig. 2. It …

Simple and tight complexity lower bounds for solving Rabin games

A Casares, M Pilipczuk, M Pilipczuk, US Souza… - 2024 Symposium on …, 2024 - SIAM
… We study Rabin games defined as follows. The arena of a Rabin game is a (finite) directed
graph D … Rabin games and colourful universal trees. Unpublished, 2023. [Pit06] Nir Piterman. …

Deciding regular games: a playground for exponential time algorithms

Z Liang, B Khoussainov, M Xiao - arXiv preprint arXiv:2405.07188, 2024 - arxiv.org
… , eg, Muller games, Rabin games or Streett games, and studies the … In the following, we
apply binary trees to maintain sets of … Thejaswini, Rabin games and colourful universal trees, in …

On the minimisation of transition-based Rabin automata and the chromatic memory requirements of Muller conditions

A Casares - arXiv preprint arXiv:2105.12009, 2021 - arxiv.org
… of chromatic memory required in games using a given Muller … The colours defining the Rabin
condition are all pairs of … We prove that T is the Zielonka tree of F by induction. We suppose …

A direct symbolic algorithm for solving stochastic Rabin games

T Banerjee, R Majumdar, K Mallik, AK Schmuck… - … Conference on Tools …, 2022 - Springer
… We define the existential, universal, and controllable predecessor operators as follows. For
S ⊆ … Infinite games on finitely coloured graphs with applications to automata on infinite trees. …