By Paul Levy
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Additional info for Lecons d'analyse fonctionnelle, professes au College de France, par Paul Levy,... avec une preface de M. J. Hadamard
The sequence of actions illustrated in Figure 15 is hence derived. Figure 15. The aggregated form of ‘‘First row’’ strategy Moves States 1, 2 A B 3, 5 A A B 7, 8 B A Up B 13, 19 Right A Left 14, 20 B 4, 6 Moves States B Down A Up B Down 15, 21 B Left 16, 22 A 9, 11 B Right 10, 12 B A Down, 17, 23 A B A Left, Right Up Left, Right 18, 24 A B Decomposition Patterns in Problem Solving 41 Here the categories are AB##, A#B#, #AB#, ##AB#, BA# y , respectively; here, too, the problem consists in establishing an order in terms of proximity to the goal.
Therefore the player classiﬁes the building blocks according to an order that deﬁnes the relative distances to the goal. This clariﬁes the reasons why errors appear: if such a system of distances deﬁned at an abstract level of representation is isomorphic with the minimal distances that are obtained by applying the backward branching procedure to the extended description, then the decomposition in Bi blocks is optimal while – if this is not the case – the decomposition will introduce hidden errors.
1 At every step a subproblem is proposed; the starting and ending positions that deﬁne every subproblem are sets of configurations that we will call ‘‘building blocks’’; for example at the end of the step two in the example above, the building block is the set of conﬁgurations where there are ‘‘the top-layer pieces in the correct spot but not necessarily in the correct orientation’’. Every subproblem is therefore characterized by a pair of building blocks, respectively representing the class of starting conﬁgurations and the class of ending conﬁgurations.
Lecons d'analyse fonctionnelle, professes au College de France, par Paul Levy,... avec une preface de M. J. Hadamard by Paul Levy