Strategy construction using homomorphisms between games

Banerji, Ranan B.; Ernst, George W.

doi:10.1016/0004-3702(72)90050-1

Cited by 14 publications

(20 citation statements)

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“…However, we do need to know the applicability condition for the Nimlike method. This condition was discovered by Dunning [6] and is also described in [2]. Both references give a formal justification of the condition; in this paper we present the condition without justification.…”

Section: Applicability Condition For the Nim-like Methodmentioning

confidence: 90%

“…Of course, the inputs are not specified schematically, because Oyen's program removes all schema variables in generating primitive invariants; for example, s(l) is given as a primitive invariant for move (3,2).…”

Section: Discussionmentioning

confidence: 99%

“…This invariant is quite general, because it implies that s(2, 0) • s (2,4) is Invariant as well as s(2, 0) + s (2,4). This step of the process generates the four invariants…”

Section: Classes Of Problem-solving Strategiesmentioning

confidence: 92%

“…The letters in this figure represent arbitrary but fixed constants (which denote the integers on the disks). The application of rotate (2,4) to this state produces Figure 5b.…”

Section: Classes Of Problem-solving Strategiesmentioning

confidence: 95%

“…The program considers the first conjunct of (2), which has a left-hand side of s(2, 0). Next it looks for a primitive mvariant that contains s(2, 0) and finds s(2, 0) + s (2,4). Then DGBS looks for a conjunct of(2) with s(2, 4) on the left-hand side and finds s(2, 4) = 12 -s(l, 4) -s(3, 4) -s(4, 4).…”

Section: Generating Rowmentioning

confidence: 99%

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Mechanical Discovery of Classes of Problem-Solving Strategies

Ernst

Goldstein

1982

J. ACM

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This research assumes that a problem-solving method has an applicabdtty condmon which specifies the properties of "good" problem-dependent parameters for the method Such a condition Is used as the basis of a computer program that mechamcally generates good parameters for the method to use in solving the problem Such problem-dependent parameters for a method constitute a problem-solving strategy.To show the feastbdity of this approach, it is used on two different methods' the GPS method for solving problems and the Nim-hke method for playing games That as, for each is constructed a program that generates good problem-dependent parameters for the input problem (or game) speclficaUon. These programs and their empirical results on a number of different problems and games are described The programs appear to be reasonably efficient and powerful In pamcular, each discovered some nonobvlous strategies Categories and Subject Descriptors 1.2 6 [Artificial Intelligence] Learning--parameter learning 1 2 8 [Artificial Intelligence] Problem Solving, Control Methods and Search--heunsuc methods

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Section: Applicability Condition For the Nim-like Methodmentioning

confidence: 90%

Section: Discussionmentioning

confidence: 99%

“…This invariant is quite general, because it implies that s(2, 0) • s (2,4) is Invariant as well as s(2, 0) + s (2,4). This step of the process generates the four invariants…”

Section: Classes Of Problem-solving Strategiesmentioning

confidence: 92%

“…The letters in this figure represent arbitrary but fixed constants (which denote the integers on the disks). The application of rotate (2,4) to this state produces Figure 5b.…”

Section: Classes Of Problem-solving Strategiesmentioning

confidence: 95%

Section: Generating Rowmentioning

confidence: 99%

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