A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Filters
Time-Optimal Winning Strategies for Poset Games
[chapter]
2009
Lecture Notes in Computer Science
Preserved Fulltext
We show that optimal strategies (with respect to long term average accumulated waiting times) exist. ...
We introduce a novel winning condition for infinite two-player games on graphs which extends the request-response condition and better matches concrete applications in scheduling or project planning. ...
I want to thank him for his advice and suggestions. Also, I want to thank the anonymous referees of [8] for their helpful remarks. ...
doi:10.1007/978-3-642-02979-0_25
fatcat:kx3qaoejsndydizasrcskawjsm
Strategy-Stealing is Non-Constructive
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We prove that this problem is PSPACE-hard already for Minimum Poset Games and Symmetric Maker-Maker Games, which are simple classes of games that capture two of the main types of strategy-stealing arguments ...
In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. ...
to 2 . • Output: any optimal first move for the first player in the associated game. ...
arXiv:1911.06907v1
fatcat:7zfvsscqjfejrdwuqo3skqzbve
Strategy-Stealing Is Non-Constructive
2020
Innovations in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We prove that this problem is PSPACE-Complete already for Minimum Poset Games and Symmetric Maker-Maker Games, which are simple classes of games that capture two of the main types of strategy-stealing ...
In many combinatorial games, one can prove that the first player wins under best play using a simple but non-constructive argument called strategy-stealing. ...
Theorem 2 generalizes to show that any minimum poset game is a win for the first player. ...
doi:10.4230/lipics.itcs.2020.21
dblp:conf/innovations/BodwinG20
fatcat:4fnuixrygzff5nhdzdh3fnmk54
Chain-making games in grid-like posets
2012
Journal of Combinatorics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2012; you can also visit the original URL.
The file type is application/pdf.
We study the Maker-Breaker game on the hypergraph of chains of fixed size in a poset. ...
game. ...
To show optimality of the resulting strategy for Maker, we present a strategy for Breaker. ...
doi:10.4310/joc.2012.v3.n4.a3
fatcat:horpht2prfbulergkf36blq4aq
Chain-making games in grid-like posets
[article]
2011
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We study the Maker-Breaker game on the hypergraph of chains of fixed size in a poset. ...
game. ...
To show optimality of the resulting strategy for Maker, we present a strategy for Breaker. ...
arXiv:1108.0710v1
fatcat:vzhkzci3fbenjn4kj5gixolkzu
Asymmetric Coloring Games on Incomparability Graphs
2015
Electronic Notes in Discrete Mathematics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The game chromatic number of G is the minimum number of colors that allows Alice to win the game. ...
In this extended abstract, we study the behavior of these parameters for incomparability graphs of posets with bounded width. ...
The game chromatic number of G, denoted by χ g (G), is the minimum number of colors for which Alice has a winning strategy in the coloring game on G. ...
doi:10.1016/j.endm.2015.06.108
fatcat:lhwz25z73jgefeaj65jostre3e
Combinatorial Game Complexity: An Introduction with Poset Games
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this introduction we develop the fundamentals of combinatorial game theory and focus for the most part on poset games, of which Nim is perhaps the best-known example. ...
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. ...
We say that a poset P is an ∃-game (or winning position) if the first player has a winning strategy, and P is a ∀game (or losing position) if the second player has a winning strategy. ...
arXiv:1505.07416v2
fatcat:yxcmoncmpvailp27irc7e3ydbi
Asymmetric coloring games on incomparability graphs
[article]
2015
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We study the behavior of these parameters for incomparability graphs of posets with bounded width. ...
The game chromatic number of G is the minimum number of colors that allows Alice to win the game. ...
The game chromatic number of G, denoted by χ g (G), is the minimum number of colors for which Alice has a winning strategy in the coloring game on G. ...
arXiv:1503.04748v1
fatcat:kqmmyg4ndzd2bc3sgefq32ewru
Counterexamples to Conjectures About Subset Takeaway and Counting Linear Extensions of a Boolean Lattice
2017
Order
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We develop an algorithm for efficiently computing recursively defined functions on posets. ...
We illustrate this algorithm by disproving conjectures about the game Subset Takeaway (Chomp on a hypercube) and computing the number of linear extensions of the lattice of a 7-cube and related lattices ...
The first is that of finding the optimal strategy for the game of Chomp (or Subset Takeaway). The second is that of counting the number of linear extensions. ...
doi:10.1007/s11083-017-9431-6
fatcat:42nx3sp6xzhmvp6szuhnkoujpe
Pomax games - a family of partizan games played on posets
[article]
2014
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We prove that pomax games are always integer-valued and for colored tree posets and chess-colored Young diagram posets we give a simple formula for the value of the game. ...
However, for pomax games on general posets of height 3 we show that the problem of deciding the winner is PSPACE-complete and for posets of height 2 we prove NP-hardness. ...
So, if Black starts playing the game G − G L − 1 we must show that White has a winning strategy. ...
arXiv:1405.1914v1
fatcat:jagpx53c6jh25jmaat5vuac64u
Numerical Tic-Tac-Toe on the 4×4 Board
[chapter]
2014
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
In this paper we consider the 4 × 4 game and determine that the second player has the advantage. ...
The original 3 × 3 game was created and analyzed by Ron Graham nearly fifty years ago and has been shown that the first player has the advantage. ...
By using an appropriately pruned tree for the question "Can player two force a win?" we would have a perfect strategy for the game. ...
doi:10.1007/978-3-319-08783-2_46
fatcat:fyc4jhrahbeelasxnx2uihpod4
Small Resolution Proofs for QBF using Dependency Treewidth
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Dependency treewidth pushes the frontiers of tractability for QBF by overcoming the limitations of previously introduced variants of treewidth for QBF. ...
This is especially true for the structural parameter treewidth, which has allowed the design of successful algorithms for SAT but cannot be straightforwardly applied to QBF since it does not take into ...
The authors wish to thank the anonymous reviewers for their helpful comments. Eduard Eiben acknowledges support by the Austrian Science Fund (FWF, projects P26696 and W1255-N23). ...
arXiv:1711.02120v1
fatcat:dvyygn3dyrdudn7hqchxyg53j4
Page 2072 of Mathematical Reviews Vol. , Issue 2003C
[page]
2003
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
A master for one of these games is an agent who plays a winning strategy. ...
However, if in addition to getting a program, a machine may also watch masters play winning strategies, then the machine is able to incrementally learn a winning strategy for the given game. ...
Complexity, appeal and challenges of combinatorial games
2004
Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
For algorithmicians, such studies provide new interesting algorithmic challenges. ...
Substantiations of these assertions are illustrated on hand of many sample games, leading to a deÿnition of the tractability, polynomiality and e ciency of subsets of games. ...
Yet, for annihilation games, the only strategy that we know which can produce a next winning move from an N -position in polynomial time, is a strategy in the broad sense. ...
doi:10.1016/j.tcs.2002.11.001
fatcat:iay4nt562re2xniyhtt6l2p2cy
Isolating Cardinal Invariants
[article]
2001
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
There is an optimal way to increase certain cardinal invariants of the continuum. ...
This is obviously a winning strategy for Adam. ...
For the left to right direction fix a winning strategy σ for Adam. ...
arXiv:math/0106202v1
fatcat:rmfsrf2bdjhobkxec35j3fcwqi
« Previous
Showing results 1 — 15 out of 252 results