Draws, Zugzwangs, and PSPACE-Completeness in the Slither Connection Game

Bonnet, Édouard; Jamain, Florian; Saffidine, Abdallah

doi:10.1007/978-3-319-27992-3_15

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…If so, the success of this work will make it more likely to solve 7x7 kill-all Go entirely. • Apply RZS to other goal-achieving problems for other games, such as Gomoku, Connect6 and Slither (Bonnet, Jamain, and Saffidine 2015), and even other domain of applications. • Incorporate RZS into other search algorithms, such as proof-number search (Allis 1994;Nagai 2002) or alphabeta search (Knuth and Moore 1975).…”

Section: Discussionmentioning

confidence: 99%

A Novel Approach to Solving Goal-Achieving Problems for Board Games

Chung-Chin¹,

Wu²,

Wei³

et al. 2022

AAAI

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Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is well-studied is the category of life-and-death (L&D) problems for Go, which helps players hone their skill of identifying region safety. Many previous methods like lambda search try null moves first, then derive so-called relevance zones (RZs), outside of which the opponent does not need to search. This paper first proposes a novel RZ-based approach, called the RZ-Based Search (RZS), to solving L&D problems for Go. RZS tries moves before determining whether they are null moves post-hoc. This means we do not need to rely on null move heuristics, resulting in a more elegant algorithm, so that it can also be seamlessly incorporated into AlphaZero's super-human level play in our solver. To repurpose AlphaZero for solving, we also propose a new training method called Faster to Life (FTL), which modifies AlphaZero to entice it to win more quickly. We use RZS and FTL to solve L&D problems on Go, namely solving 68 among 106 problems from a professional L&D book while a previous state-of-the-art program TSUMEGO-EXPLORER solves 11 only. Finally, we discuss that the approach is generic in the sense that RZS is applicable to solving many other goal-achieving problems for board games.

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Section: Discussionmentioning

confidence: 99%

A Novel Approach to Solving Goal-Achieving Problems for Board Games

Chung-Chin¹,

Wu²,

Wei³

et al. 2022

AAAI

View full text Add to dashboard Cite

show abstract

“…Slither is also a connection game play on an n × n square board, in which stones can be placed on unoccupied grids and moved. It has been shown that the game is PSPACE-complete and cannot end in a draw (Bonnet, Jamain, and Saffidine 2015). Like the game of Hex, the first player who connects its own sides (e.g., up/down for White) wins.…”

Section: Rzs For the Game Of Slithermentioning

confidence: 99%

“…However, the diagonal (D5, E4) is legal in (e) since D4 connects to both via a direct adjacency. This restriction is called the diagonal rule (Bonnet, Jamain, and Saffidine 2015).…”

Section: Rzs For the Game Of Slithermentioning

confidence: 99%

A Novel Approach to Solving Goal-Achieving Problems for Board Games

Chung-Chin¹,

Wu²,

Wei³

et al. 2021

Preprint

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Goal-achieving problems are puzzles that set up a specific situation with a clear objective. An example that is wellstudied is the category of life-and-death (L&D) problems for Go, which helps players hone their skill of identifying region safety. Many previous methods like lambda search try null moves first, then derive so-called relevance zones (RZs), outside of which the opponent does not need to search. This paper first proposes a novel RZ-based approach, called the RZ-Based Search (RZS), to solving L&D problems for Go. RZS tries moves before determining whether they are null moves post-hoc. This means we do not need to rely on null move heuristics, resulting in a more elegant algorithm, so that it can also be seamlessly incorporated into AlphaZero's superhuman level play in our solver. To repurpose AlphaZero for solving, we also propose a new training method called Faster to Life (FTL), which modifies AlphaZero to entice it to win more quickly. We use RZS and FTL to solve L&D problems on Go, namely solving 68 among 106 problems from a professional L&D book while a previous program solves 11 only. Finally, we discuss that the approach is generic in the sense that RZS is applicable to solving many other goal-achieving problems for board games.

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On the complexity of connection games

Bonnet

Jamain

Saffidine

2016

Theoretical Computer Science

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In this paper, we study three connection games among the most widely played: havannah, twixt, and slither. We show that determining the outcome of an arbitrary input position is PSPACE-complete in all three cases. Our reductions are based on the popular graph problem generalized geography and on hex itself. We also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is W[1]-hard, short hex is FPT. Finally, we prove that the ultra-weak solution to the empty starting position in hex cannot be fully adapted to any of these three games.

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Draws, Zugzwangs, and PSPACE-Completeness in the Slither Connection Game

Cited by 3 publications

References 8 publications

A Novel Approach to Solving Goal-Achieving Problems for Board Games

A Novel Approach to Solving Goal-Achieving Problems for Board Games

A Novel Approach to Solving Goal-Achieving Problems for Board Games

On the complexity of connection games

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