A Theory of Heuristic Information in Game-Tree Search by Chun-Hung Tzeng

By Chun-Hung Tzeng

Searching is a crucial procedure in so much AI platforms, in particular in these AI construction structures such as an international database, a collection of creation principles, and a regulate approach. due to the intractability of uninformed seek tactics, using heuristic details is important in such a lot looking out techniques of AI structures. this significant proposal of heuristic informatioD is the valuable subject of this booklet. We first use the 8-puzzle and the sport tic-tac-toe (noughts and crosses) as examples to assist our dialogue. The 8-puzzle involves 8 numbered movable tiles set in a three x three body. One mobilephone of the body is empty in order that it really is attainable to maneuver an adjoining numbered tile into the empty mobilephone. Given tile configurations, preliminary and objective, an 8-puzzle challenge includes altering the preliminary configuration into the objective configuration, as illustrated in Fig. 1.1. an answer to this challenge is a series of strikes top from the preliminary configuration to the objective configuration, and an optimum answer is an answer having the smallest variety of strikes. now not all difficulties have strategies; for instance, in Fig. 1.1, challenge 1 has many ideas whereas challenge 2 has no resolution at all.

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Another essential concept, a probability measure on a Borel field, is introduced in the next section. 2 Probability Spaces Let Q be a space, and let F be a Borel field on Q. A probability measure is defined as follows. 2. A probability measure P on F is a numerically valued set function with domain F, satisfying the following axioms: (1) P(A)20 for any A EF. (2) If {AJ is a countable collection of pairwise disjoint sets in F, then P(u;A;) =L;P(AJ (3) P (Q)= 1. Let P be a probability measure on F; then the triple (Q, P, F) is called a probability space.

Therefore, with our formulation of heuristic information, we can compare and accumulate heuristic information. A heuristic search is defined as a function which returns (at each node) a piece of heuristic information about the game being searched. A conventional static evaluation function is a special heuristic search under this definition. In a search tree, we 52 Heuristic Information accumulate heuristic information (by means of the intersection operation) at all of the nodes in the search tree.

The mean is also called the expectation of the random variable. In a probability space (Q, P, F), a concept of integration with respect to the probability measure can be introduced, similar to the usual integration of realvalued functions on the real line. Let f be a random variable, and let A be a measurable set. Then the integral of f over A is denoted by ff A dP . 34 Probability Spaces and Martingales Without giving the definition of integration in detail, we list here some properties needed in our discussion.

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