Proof-Number Search and Transpositions

  title={Proof-Number Search and Transpositions},
  author={Martin Schijf and L. Victor Allis and Jos Uiterwijk},
  journal={J. Int. Comput. Games Assoc.},

Minimal Proof Search for Modal Logic K Model Checking

This work presents MPS, an effort number based algorithm solving the model checking problem for MMLK, and proves two important properties for MPS beyond its correctness: the (dis)proof exhibited by MPS is of minimal cost for a general definition of cost, and the algorithm is an optimal algorithm for finding (Dis)proofs of minimalcost.

Developments on Product Propagation

Three domains where, for generic non-optimized versions of Product Propagation, pp performs better than previously known algorithms for solving games are exhibited.

Applying Proof-number Search to Chess 0s0z0z0z Z0z0z0ok 0z0z0o0z Z0z0o0z0 0a0o0z0m Z0z0z0z0 Pzpzpo0z Zkz0zbz0

This contribution shows that pn-search is a highly capable searcher for mates in chess and achieves its results without using any heuristic chess knowledge, and discusses how pN-search can be applied to general tactical searches.

Towards solving the 7-in-a-row game

This paper presents a number of heuristic improvements to Proof Number Search and examines their effect within the context of this particular game, the 7-in-a-row game.

On Computation Complexity of True Proof Number Search

  • Chao Gao
  • Computer Science, Mathematics
  • 2021
We point out that the computation of true proof and disproof numbers for proof number search in arbitrary directed acyclic graphs is NP-hard, an important theoretical result for proof number search.

Automated Synthetic Feasibility Assessment: A Data-driven Derivation of Computational tools for Medicinal Chemistry

This thesis describes a mapping between organic synthesis and heuristic search and builds a planner that can solve such problems automatically at the undergraduate level and shows the need for powerful heuristicsearch algorithms and large databases of synthetic information, which are used to derive a qualitatively new kind of heuristic guidance.

Solving Games and All That

This work presents a formal framework to represent best-first search algorithms, and proposes an extension of this technique for stacked-matrix games, a generalization of zero-sum perfect information two-player games that allows simultaneous moves.

Computers and Games

This paper is the first attempt to apply dependency-based search to Connect6 programs, and the targeted program is NCTU6, which won Connect6 tournaments in the Computer Olympiad twice and defeated many professional players in Man-Machine Connect6 championships.

Multiple-Outcome Proof Number Search

Experimental results on solving various positions of the games CONNECT FOUR and WOODPUSH show that in most problems, the total number of node creations of MOPNS is lower than the cumulative number of nodes creations of PNS, even in the best case where PNS does not need to perform a binary search.



Qubic Solved Again

  • Heuristic Programming in Arti cial
  • 1992

A Knowledge-Based Ap

  • 1990

Proof-Number Search

Zur Theorie der Gesellschaftsspiele

Conspiracy Numbers for Min-Max Search

Chess Skill in Man and Machine

  • P. Frey
  • Computer Science
    Springer New York
  • 1983
The heuristic search: An alternative to the alpha-beta minimax procedure and chess thinking: Man versus machine.

An Analysis of Alpha-Beta Pruning

Searching for solutions in games and artificial intelligence

Applying Retrograde Analysis to Nine Men's Morris

Some of the optimal play in Nine Men's Morris is clearly beyond human ability, sometimes requiring over 150 plies of seemingly random moves before a win is reached.