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Justifications and a Reconstruction of Parity Game Solving Algorithms [article]

Ruben Lapauw, Maurice Bruynooghe, Marc Denecker
2021 arXiv   pre-print
Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification.  ...  This paper defines parametrized parity games and introduces an operation, Justify, that determines a winning strategy for a single node.  ...  We start the paper with a short description of the role of parity game solvers in the domain of formal verification (Section 2).  ... 
arXiv:2102.01440v1 fatcat:njznbfbf55ggnofxjpcryoezci

Priority Promotion with Parysian Flair [article]

Massimo Benerecetti
2021 arXiv   pre-print
We develop an algorithm that combines the advantages of priority promotion - one of the leading approaches to solving large parity games in practice - with the quasi-polynomial time guarantees offered  ...  After Parys' Solver is run (with full precision) for a parity game with maximal priority p max , u −1 (p max + 1) contains the winning region of player p max mod 2. ▶ Lemma 14.  ...  The parity games encoding have been obtained with the tool MLSolver [28] .  ... 
arXiv:2105.01738v2 fatcat:m4u76cm3vrfnbiu4flje4swmqa

From Quasi-Dominions to Progress Measures [article]

Massimo Benerecetti, Daniele Dell'Erba, Marco Faella, Fabio Mogavero
2021 arXiv   pre-print
We revisit the approaches to the solution of parity games based on progress measures and show how the notion of quasi dominions can be integrated with those approaches.  ...  justifications FPJ [34] .  ...  The benchmarks include worst-case games for the considered solvers and clustered random games generated with the PGSolver framework [18] .  ... 
arXiv:2008.04232v2 fatcat:yerwrduwcbadtfouhpgstc46qu

Exploiting Game Theory for Analysing Justifications

2020 Theory and Practice of Logic Programming  
The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games.  ...  The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results.  ...  Additionally, justifications were used to improve parity game solvers (Lapauw et al. 2020) .  ... 
doi:10.1017/s1471068420000186 fatcat:7ivdncdeozh3dklfb364v7k5lu

Exploiting Game Theory for Analysing Justifications [article]

Simon Marynissen, Bart Bogaerts, Marc Denecker
2020 arXiv   pre-print
In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory.  ...  We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions.  ...  Additionally, justifications were used to improve parity game solvers (Lapauw et al. 2020) .  ... 
arXiv:2008.01609v1 fatcat:tgknop7zefhatb3wpcrhr3ev2q

A scalable verification solution for blockchains [article]

Jason Teutsch, Christian Reitwießner
2019 arXiv   pre-print
Our new system consists of a financial incentive layer atop a dispute resolution layer where the latter takes form of a versatile "verification game."  ...  In addition to secure outsourced computation, immediate applications include decentralized mining pools whose operator is an Ethereum smart contract, a cryptocurrency with scalable transaction throughput  ...  Otherwise the Solver must play the verification game with the challenging Verifier(s).  ... 
arXiv:1908.04756v1 fatcat:mrywp4eswjfwbbmwsllbeadspy

Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language

Mitchell J. Nathan, Candace Walkington
2017 Cognitive Research  
Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education,  ...  Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action  ...  GEMC theory, along with findings from , served as the basis for the design of a scalable video game environment that would guide directed actions in service of players' proofs and justifications for mathematical  ... 
doi:10.1186/s41235-016-0040-5 pmid:28217739 pmcid:PMC5285420 fatcat:5h3iqdjqk5h45ktzt7jkpedzk4

Seeking or Skipping Regularities? Novice Tendencies and the Role of Invariants

2003 Informatics in Education. An International Journal  
Some solutions were incorrect, others were inefficient, and some had no convincing justification.  ...  Due to their implicit nature, invariants may be less apparent to algorithmic problem solvers. Yet, invariants are essential for designing correct and efficient algorithms.  ...  This is the case for example in the Game task of IOI'96 (The International Olympiad in Informatics -a Game, 1996) , where the operator is "line-end removal", and in the Median Task of IOI'2000 (Horvath  ... 
doi:10.15388/infedu.2003.16 fatcat:3n5jkanm7vekxlefm3quryh4ja

Experimental Aspects of Synthesis

Rüdiger Ehlers
2011 Electronic Proceedings in Theoretical Computer Science  
Also, there are two other publications [66, 51] reporting on experimental results for synthesis approaches using generalized parity games.  ...  If it can be shown that the other approaches do not even terminate with a timeout of B for each step, additional justification for the new approach is obtained.  ... 
doi:10.4204/eptcs.50.1 fatcat:oyu6j7pugjev3eybhzgpujuh4u

Fixpoint Games on Continuous Lattices [article]

Paolo Baldan, Barbara König, Tommaso Padoan, Christina Mika-Michalski
2021 arXiv   pre-print
For powerset lattices the fixpoint game is intimately connected with classical parity games for μ-calculus model-checking, whose solution can exploit as a key tool Jurdziński's small progress measures.  ...  A simple parity game, referred to as fixpoint game, is defined that provides a correct and complete characterisation of the solution of equation systems over continuous lattices, a quite general class  ...  Furthermore we are grateful to Clemens Kupke for bringing fixpoint games to our attention.  ... 
arXiv:1810.11404v2 fatcat:eazlulkcdfhzte44tldfzghei4

Real World Games Look Like Spinning Tops [article]

Wojciech Marian Czarnecki, Gauthier Gidel, Brendan Tracey, Karl Tuyls, Shayegan Omidshafiei, David Balduzzi, Max Jaderberg
2020 arXiv   pre-print
We hypothesise that their geometrical structure resemble a spinning top, with the upright axis representing transitive strength, and the radial axis, which corresponds to the number of cycles that exist  ...  This paper investigates the geometrical properties of real world games (e.g. Tic-Tac-Toe, Go, StarCraft II).  ...  We are also thankful to authors of OpenSpiel framework for the help provided with setting up the experiments that allowed empirical validation of the hypothesised geometry.  ... 
arXiv:2004.09468v2 fatcat:qkmirywdtzdohfaryyqi5tqpey

The Overlooked Don't-Care Notion in Algorithmic Problem Solving

2009 Informatics in Education. An International Journal  
In this paper, we illuminate and elaborate on this notion with six algorithmic illustrations, and describe our experience with novice difficulties with respect to this notion.  ...  The above game solution is based on the idea that we do not care for some of the game information -the sizes and the parities of the largest K − 1 piles during the game.  ...  Devise a strategy for winning the game. In our experience, many students like this kind of tasks, as it involves a game, which they may play with each other.  ... 
doaj:c419318617754d55904ef2c17ae695ac fatcat:4qh6lvpbavfwvdjia3a2cn343a

Lower Bounds

Olaf Beyersdorff, Ilario Bonacina, Chew Leroy
2016 Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science - ITCS '16  
SAT and QBF solvers are powerful algorithms that efficiently solve the classically hard problems of SAT and QBF for large classes of practically relevant formulas, with modern solvers routinely solving  ...  In fact, this upper bound can be improved to AC 0 [2 ]-Frege + ∀red, albeit not for arbitrary NC 1 -encodings of Parity, as it is not clear how these could be handled in bounded depth.  ... 
doi:10.1145/2840728.2840740 dblp:conf/innovations/BeyersdorffBC16 fatcat:bhoydv233rgo3gnpc6hgdto76u

Tradeoffs in the complexity of backdoors to satisfiability: dynamic sub-solvers and learning during search

Bistra Dilkina, Carla P. Gomes, Ashish Sabharwal
2014 Annals of Mathematics and Artificial Intelligence  
These syntactic classes, however, do not capture key aspects of solvers such as empty clause (i.e., violated constraint) detection.  ...  Others, such as backdoor sets, are of interest because they capture key aspects of state-of-the-art constraint solvers as well as of many real-world problem instances.  ...  G is called a graphical game; when the payoffs of all players depend on the actions of all other players, the graphical game degenerates into a classical "full-interaction" game.  ... 
doi:10.1007/s10472-014-9407-9 fatcat:twcqxbtbybd2xmviixsstjhloa

Symbolic Parity Game Solvers that Yield Winning Strategies [article]

Oebele Lijzenga
2020 pre-print
Parity games play an important role for LTL synthesis as evidenced by recent breakthroughs on LTL synthesis, which rely in part on parity game solving.  ...  Current symbolic parity game solving algorithms do not yield winning strategies.  ...  They are called distractions because (many) parity game solvers will initially assume that these vertices are safe for player α to play to, but after some steps, the parity game solver will find that these  ... 
doi:10.4204/eptcs.326.2 arXiv:2009.10876v1 fatcat:dzlzq7sgkfd3bfl2xsummtmvta
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