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Fixed-Point Logics and Solitaire Games

Dietmar Berwanger, Erich Gr�del
2004 Theory of Computing Systems  
The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time.  ...  On finite structures (but not on infinite ones), Solitaire-LFP is equivalent to transitive closure logic. We also consider the solitaire fragment of guarded fixed-point logics.  ...  We define Solitaire-LFP, a fragment of least fixed-point logic, whose model-checking games are nested solitaire games, and we analyse the algorithmic properties and the expressive power of this fragment  ... 
doi:10.1007/s00224-004-1147-5 fatcat:o7bj3ruwkzgxxdqqnsdcboehpm

Large Peg-Army Maneuvers [article]

Luciano Gualà, Stefano Leucci, Emanuele Natale, Roberto Tauraso
2016 arXiv   pre-print
In this paper, we consider two problems with an algorithmic flavour which are related with this game, namely Solitaire-Reachability and Solitaire-Army.  ...  Despite its long history, the classical game of peg solitaire continues to attract the attention of the scientific community.  ...  We study the former problem from a computational point of view and we prove that Solitaire-Reachability is NP-complete.  ... 
arXiv:1603.00898v2 fatcat:rwlztozq5rc7lc64calqxqegni

Characterizing Predicate Arity and Spatial Structure for Inductive Learning of Game Rules [chapter]

Debidatta Dwibedi, Amitabha Mukerjee
2015 Lecture Notes in Computer Science  
Knowledge from spatial structure and semantic graphs is mapped to FOL descriptions of the moves and used in an Inductive Logic framework to infer the valid moves and other rules of the game.  ...  Given a set of videos for a game, we use an improved 3D multi-object tracking to obtain the positions of each piece in games such as 4-peg solitaire or Towers of Hanoi.  ...  Thus, the background input for inductive logic programming invariably involves predicates with fixed arities.  ... 
doi:10.1007/978-3-319-16181-5_23 fatcat:hw3jvndujbbs5i77224c7kp2me

Learning from natural instructions

Dan Goldwasser, Dan Roth
2013 Machine Learning  
We evaluate our approach by applying it to the rules of the solitaire card game.  ...  We show that our learning approach can eventually use natural language instructions to learn the target concept and play the game legally.  ...  The game-related resources used in the training process amount to the small and fixed set of labeled game moves used by the feedback function.  ... 
doi:10.1007/s10994-013-5407-y fatcat:hwtlnkvfd5gklijltazvrzeuuy

Algorithms for Parity Games [chapter]

Hartmut Klauck
2002 Lecture Notes in Computer Science  
with finite arenas and other two-player games.  ...  In a play of the game a token is placed on the starting vertex and is then moved over the graph by Player 0 and Player 1, each making their move if the token is on one of their vertices.  ...  Now we have a correspondence between fixed points and game progress measures. We are interested in a game progress measure inducing the winning region.  ... 
doi:10.1007/3-540-36387-4_7 fatcat:2xu24otqbzarfpfetg5574blza

Acyclic Constraint Logic and Games [article]

Hendrik Jan Hoogeboom, Walter A. Kosters, Jan N. van Rijn, Jonathan K. Vis
2016 arXiv   pre-print
We focus on the acyclic version, apply this to Klondike, Mahjong Solitaire and Nonogram (that requires planarity), and discuss the more complicated game of Dou Shou Qi.  ...  Non-deterministic Constraint Logic is a family of graph games introduced by Demaine and Hearn that facilitates the construction of complexity proofs.  ...  First we explain the different types of graph games. Next we apply these to the games Klondike, Mahjong Solitaire, Nonogram and Dou Shou Qi.  ... 
arXiv:1604.05487v1 fatcat:remx3tdn6ncwpflqyenepjdgaq

On-The-Fly Solving for Symbolic Parity Games [article]

Maurice Laveaux, Wieger Wesselink, Tim A.C. Willemse
2022 arXiv   pre-print
In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an exploration.  ...  We implement our techniques for symbolic parity games and study their effectiveness in practice, showing that speed-ups of several orders of magnitude are feasible and overhead (if unavoidable) is typically  ...  Acknowledgements We would like to thank Jeroen Meijer and Tom van Dijk for their help regarding the Sylvan library when implementing our prototype.  ... 
arXiv:2201.09607v1 fatcat:zulfhot6efeypnv6pnsvd7drje

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory [article]

Erik D. Demaine, Robert A. Hearn
2008 arXiv   pre-print
In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness  ...  Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open.  ...  Acknowledgments Comments from several people have helped make this survey more comprehensive, including Martin Demaine, Azriel Fraenkel, Martin Kutz, and Ryuhei Uehara.  ... 
arXiv:cs/0106019v2 fatcat:lae3nzasxvbsljdya7bu3t64ou

Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

Maciej Gazda, Tim A.C. Willemse
2013 Electronic Proceedings in Theoretical Computer Science  
exponential time to solve dull games and (nested) solitaire games.  ...  Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems.  ...  These include model checking problems for fixed point logics [5] , behavioural equivalence checking problems [4] and satisfiability and synthesis problems [1] .  ... 
doi:10.4204/eptcs.119.4 fatcat:scbv7t6dobh37ekv5iokhjthqq

Defining Winning Strategies in Fixed-Point Logic

Felix Canavoi, Erich Gradel, Simon Lessenich, Wied Pakusa
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
A closely related, yet different, facet of this problem concerns the definability of winning regions and winning strategies in logical systems such as monadic second-order logic, least fixed-point logic  ...  The quest for efficient algorithmic constructions of winning regions and winning strategies in infinite games, in particular parity games, is of importance in many branches of logic and computer science  ...  are fixed-points logics such as LFP and IFP.  ... 
doi:10.1109/lics.2015.42 dblp:conf/lics/CanavoiGLP15 fatcat:3cndjmbxujgelmx63y7piyakqq

Playing with Triangulations [chapter]

Oswin Aichholzer, David Bremner, Erik D. Demaine, Ferran Hurtado, Evangelos Kranakis, Hannes Krasser, Suneeta Ramaswami, Saurabh Sethia, Jorge Urrutia
2003 Lecture Notes in Computer Science  
We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games: constructing, transforming, and marking triangulations.  ...  In various situations, we develop polynomial-time algorithms to determine who wins a given game under optimal play, and to find a winning strategy.  ...  Fig. 3 . 3 Illustrating the technique for the All-Green Solitaire Game in convex positionLet us define the logic value b(S) to be true if, and only if, it is possible to color green all the edges of the  ... 
doi:10.1007/978-3-540-44400-8_4 fatcat:6emnwk22n5ghjdjvqsmxg42hfq

Acyclic Constraint Logic and Games

Hendrik Jan Hoogeboom, Walter A. Kosters, Jan N. van Rijn, Jonathan K. Vis
2014 ICGA Journal  
We focus on the acyclic version, apply this to Klondike, Mahjong Solitaire and Nonogram (that requires planarity), and discuss the more complicated game of Dou Shou Qi.  ...  Non-deterministic Constraint Logic is a family of graph games introduced by Demaine and Hearn that facilitates the construction of complexity proofs.  ...  First we explain the different types of graph games. Next we apply these to the games Klondike, Mahjong Solitaire, Nonogram and Dou Shou Qi.  ... 
doi:10.3233/icg-2014-37102 fatcat:jzjyx66bljhcfawlcwdylbtfmu

Nmbr9 as a Constraint Programming Challenge [article]

Mikael Zayenz Lagerkvist
2020 arXiv   pre-print
Modern board games are a rich source of interesting and new challenges for combinatorial problems. The game Nmbr9 is a solitaire style puzzle game using polyominoes.  ...  This abstract presents the game, contributes new generalized variants of the game suitable for benchmarking and testing, and describes a model for the presented variants.  ...  Acknowledgments Thanks to Magnus Gedda, Magnus Rattfeldt, and Martin Butler for interesting and informative discussions on games and search methods.  ... 
arXiv:2001.04238v1 fatcat:ocwmxdaqkrb25nzztgtktm5agq

Playing Games with Algorithms: Algorithmic Combinatorial Game Theory [chapter]

Erik D. Demaine
2001 Lecture Notes in Computer Science  
In particular, we begin with general background in Combinatorial Game Theory, which analyzes ideal play in perfect-information games, and Constraint Logic, which provides a framework for showing hardness  ...  Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open.  ...  Acknowledgments Comments from several people have helped make this survey more comprehensive, including Martin Demaine, Aviezri Fraenkel, Martin Kutz, and Ryuhei Uehara.  ... 
doi:10.1007/3-540-44683-4_3 fatcat:7zoqv6zdwzbdvn34jryyg5etim

Have a Little Patience: Let Planners Play Cards

Rabia Jilani, Andrew Crampton, Diane E. Kitchin, Mauro Vallati
2016 Workshop of the UK Planning and Scheduling Special Interest Group  
This is true for both multi-player and solitaire patience games.  ...  In this paper we envisage the exploitation of solitaire card games as a pool of interesting benchmarks.  ...  We also plan to identify domain models for other games including broad games and other logic-based combinatorial number placement puzzle games.  ... 
dblp:conf/plansig/JilaniCKV16 fatcat:l5katpknbvfqxmjnbfyvpbh4vq
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