Formal Verification of Minimax Search Algorithms Using Dafny
Using the Dafny verification system, researchers have successfully confirmed the correctness of minimax-based search algorithms that incorporate alpha-beta pruning and transposition tables. These algorithms play a crucial role in traditional game-playing engines but are intricate and finely tuned, making it challenging to identify errors through testing alone. The research presents a witness-based correctness criterion for depth-limited searches utilizing transposition tables, which indicates when the values returned can be substantiated by a clear game-tree expansion. This criterion was tested on two practical adaptations of depth-limited negamax with alpha-beta pruning and transposition tables: one variant achieved a complete mechanized correctness proof, while a concrete counterexample was created for the other. This study tackles the well-known challenges in reasoning about these algorithms and establishes a formal basis for their correctness.
Key facts
- Minimax-based search algorithms with alpha-beta pruning and transposition tables are central to classical game-playing engines.
- These algorithms are subtle, highly optimized, and notoriously difficult to reason about.
- The Dafny verification system was used for formal verification.
- A witness-based correctness criterion was introduced for depth-limited search with transposition tables.
- The criterion captures when returned values can be justified by an explicit game-tree expansion.
- Two practical variants of depth-limited negamax with alpha-beta pruning and transposition tables were analyzed.
- One variant obtained a fully mechanized correctness proof.
- For the other variant, a concrete counterexample was constructed.
Entities
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