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On the Succinctness of Alternating Parity Good-for-Games Automata [article]

Udi Boker, Denis Kuperberg, Karoliina Lehtinen, Michał Skrzypczak
2020 arXiv   pre-print
We study alternating parity good-for-games (GFG) automata, i.e., alternating parity automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the  ...  We show that this problem is PSpace-hard already for alternating automata on finite words.  ...  c b b, c Good-For-Games Alternating Automata Good-for-games (GFG) nondeterministic automata are automata in which the nondeterministic choices can be resolved without looking at the future of the word  ... 
arXiv:2009.14437v1 fatcat:shsbqdzaknb7xjds3dvc7pghva

On the Succinctness of Alternating Parity Good-For-Games Automata

Udi Boker, Denis Kuperberg, Karoliina Lehtinen, Michał Skrzypczak, Nitin Saxena, Sunil Simon
2020
We study alternating parity good-for-games (GFG) automata, i.e., alternating parity automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the  ...  We show that this problem is PSpace-hard already for alternating automata on finite words.  ...  i = ∅). 41:4 On the Succinctness of Alternating Parity Good-For-Games Automata Sizes and types of automata.  ... 
doi:10.4230/lipics.fsttcs.2020.41 fatcat:j3ic7tijp5c4pimm2malhcuqrq

Good for Games Automata: From Nondeterminism to Alternation

Udi Boker, Karoliina Lehtinen, Michael Wagner
2019 International Conference on Concurrency Theory  
We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.  ...  A word automaton recognizing a language L is good for games (GFG) if its composition with any game with winning condition L preserves the game's winner.  ...  In the first part of this article, we give a coherent account of good-for-gameness for alternating automata: we generalize all the existing definitions from nondeterministic to alternating automata, and  ... 
doi:10.4230/lipics.concur.2019.19 dblp:conf/concur/BokerL19 fatcat:w6nqhu5o2zcg3j3jcexgyi4s5y

Minimising Good-for-Games automata is NP complete [article]

Sven Schewe
2020 arXiv   pre-print
This paper discusses the hardness of finding minimal good-for-games (GFG) Buchi, Co-Buchi, and parity automata with state based acceptance.  ...  We show for the standard state based acceptance that the minimality of a GFG automaton is NP-complete for Buchi, Co-Buchi, and parity GFG automata.  ...  Many thanks to Patrick Totzke and Karoliina Lehtinen for valuable feedback, enduring and helping to erase the errors of draft versions, and pointers to beautiful related works.  ... 
arXiv:2003.11979v1 fatcat:gzhl6vi7mnf7rcokrphaakaghi

On Succinctness and Recognisability of Alternating Good-for-Games Automata [article]

Udi Boker, Denis Kuperberg, Karoliina Lehtinen, Michał Skrzypczak
2020 arXiv   pre-print
We study alternating good-for-games (GFG) automata, i.e., alternating automata where both conjunctive and disjunctive choices can be resolved in an online manner, without knowledge of the suffix of the  ...  for the GFGness problem of weak automata, and a reduction from a positive solution to the G_2 conjecture to a PTime algorithm for the GFGness problem of parity automata with a fixed index.  ...  Good-For-Games Alternating Automata Good-for-games (GFG) nondeterministic automata are automata in which the nondeterministic choices can be resolved without looking at the future of the word.  ... 
arXiv:2002.07278v1 fatcat:yktbrl5e6zclxb44helgqs4zfu

Alternating Good-for-MDP Automata [article]

Ernst Moritz Hahn and Mateo Perez and Sven Schewe and Fabio Somenzi and Ashutosh Trivedi and Dominik Wojtczak
2022 arXiv   pre-print
These are nondeterministic B\"uchi automata with a restricted type of nondeterminism, albeit not as restricted as in good-for-games automata.  ...  Rabin automata, the alternating good-for-MDP automata we produce from deterministic Streett automata are bi-linear in the the size of the deterministic automaton and its index, and can therefore be exponentially  ...  Surprisingly, there is a way to exploit alternating good-for-MDP automata with a small blow-up of k+2 for k pairs.  ... 
arXiv:2205.03243v1 fatcat:wkbw2u6wffczvey2uld67thyri

Parityizing Rabin and Streett

Udi Boker, Orna Kupferman, Avital Steinitz, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
The fact parity games are memoryless is of great importance in synthesis algorithms, where one wants to generate transducers for the winning strategies [4].  ...  A good evidence to the superiority of the parity condition in the application front is the fact that the highlight of Piterman's determinization construction for nondeterministic Büchi automata [18] has  ...  For example, while today there are several algorithms that solve parity games in time less than O(n k ) [9], the best translation of alternating parity word automata to alternating weak word automata (  ... 
doi:10.4230/lipics.fsttcs.2010.412 dblp:conf/fsttcs/BokerKS10 fatcat:q7l5cyskhfhojfwofcorhoesf4

Strategy Representation by Decision Trees in Reactive Synthesis [chapter]

Tomáš Brázdil, Krishnendu Chatterjee, Jan Křetínský, Viktor Toman
2018 Lecture Notes in Computer Science  
The decisions for a player at various states of the graph game are represented as strategies.  ...  While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision  ...  The conversion of LTL to non-deterministic Büchi automata, and nondeterministic Büchi automata to deterministic parity automata, gives rise to a parity game to solve the LTL synthesis problem.  ... 
doi:10.1007/978-3-319-89960-2_21 fatcat:ehhfdoodz5foncjsqkfzytljgq

Strategy Representation by Decision Trees in Reactive Synthesis [article]

Tomáš Brázdil, Krishnendu Chatterjee, Jan Křetínský, Viktor Toman
2018 arXiv   pre-print
The decisions for a player at various states of the graph game are represented as strategies.  ...  While the algorithmic problem for solving graph games with parity objectives has been widely studied, the most prominent data-structure for strategy representation in graph games has been binary decision  ...  The conversion of LTL to non-deterministic Büchi automata, and nondeterministic Büchi automata to deterministic parity automata, gives rise to a parity game to solve the LTL synthesis problem.  ... 
arXiv:1802.00758v2 fatcat:ay5c3pkbyzahfk2aic2tljlxeu

Resource-Aware Automata and Games for Optimal Synthesis

Corina Cîrstea
2019 Electronic Proceedings in Theoretical Computer Science  
We consider quantitative notions of parity automaton and parity game aimed at modelling resource-aware behaviour, and study (memory-full) strategies for exhibiting accepting runs that require a minimum  ...  amount of initial resources, respectively for winning a game with minimum initial resources.  ...  While standard weighted parity games as used e.g. in [3, 9, 13] make no restrictions on the alternation of ∃ and ∀ moves, nor on the weights on ∀ moves or the parities of ∀ states, any weighted parity  ... 
doi:10.4204/eptcs.305.4 fatcat:7rvy2nbqcffa5phv6lwjdy3pjy

Good-for-games $\omega$-Pushdown Automata

Karoliina Lehtinen, Martin Zimmermann
2022 Logical Methods in Computer Science  
We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far.  ...  Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages.  ...  We thank Sven Schewe and Patrick Totzke for fruitful discussions leading to the results presented in Section 6.  ... 
doi:10.46298/lmcs-18(1:3)2022 fatcat:2nm6ks4rz5efznj3bgpw6md2ay

Permutation Games for the Weakly Aconjunctive μ-Calculus [article]

Daniel Hausmann, Lutz Schröder, Hans-Peter Deifel
2018 arXiv   pre-print
We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the μ-calculus  ...  By showing that limit-deterministic parity automata can be used to recognize unsuccessful branches in pre-tableaux for the weakly aconjunctive μ-calculus, we obtain satisfiability games of size O((nk)!  ...  As they typically incur exponential blowup, good determinization procedures for automata on infinite words play a crucial role in standard decision procedures for the satisfiability problem of the µ-calculus  ... 
arXiv:1710.08996v2 fatcat:chysyaumerhwxdigm5hxzijevu

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games [article]

Wojciech Czerwiński, Laure Daviaud, Nathanaël Fijalkow, Marcin Jurdziński, Ranko Lazić, Paweł Parys
2018 arXiv   pre-print
Our main technical result is a quasi-polynomial lower bound on the size of such separating automata that nearly matches the current best upper bounds.  ...  This forms a barrier that all existing approaches must overcome in the ongoing quest for a polynomial-time algorithm for solving parity games.  ...  Acknowledgements This research has been supported by the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice). W. Czerwiński and P.  ... 
arXiv:1807.10546v2 fatcat:t4fhnths5vg47akfoqlkhzmbni

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games [chapter]

Wojciech Czerwiński, Laure Daviaud, Nathanaël Fijalkow, Marcin Jurdziński, Ranko Lazić, Paweł Parys
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
Our main technical result is a quasi-polynomial lower bound on the size of such separating automata that nearly matches the current best upper bounds.  ...  This forms a barrier that all existing approaches must overcome in the ongoing quest for a polynomial-time algorithm for solving parity games.  ...  Acknowledgements This research has been supported by the EPSRC grant EP/P020992/1 (Solving Parity Games in Theory and Practice). W. Czerwiński and P.  ... 
doi:10.1137/1.9781611975482.142 dblp:conf/soda/CzerwinskiDFJLP19 fatcat:yzvvretyr5cqzczzkuj2l4jygi

On the Problem of Computing the Probability of Regular Sets of Trees

Henryk Michalewski, Matteo Mio, Marc Herbstritt
2015 Foundations of Software Technology and Theoretical Computer Science  
(3) the probability of game languages W i,k , from automata theory, is 0 if k is odd and is 1 otherwise.  ...  We propose an algorithm which computes the probability of languages recognizable by game automata. In particular this algorithm is applicable to all deterministic automata.  ...  Game automata (see [10, 11, 21] ) are special types of alternating parity tree automata.  ... 
doi:10.4230/lipics.fsttcs.2015.489 dblp:conf/fsttcs/MichalewskiM15 fatcat:6bye6q4danfujfcmgu7e6qtdsm
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