Inhibition and young children's performance on the Tower of London task

Young children, when performing problem solving tasks, show a tendency to break task rules and produce incomplete solutions. We propose that this tendency can be explained by understanding problem solving within the context of the development of “executive functions” – general cognitive control functions, which serve to regulate the operation of the cognitive system. This proposal is supported by the construction of two computational models that simulate separately the performance of 3–4 year old and 5–6 year old children on the Tower of London planning task. We seek in particular to capture the emerging role of inhibition in the older group. The basic framework within which the models are developed is derived from Fox and Das’ Domino model [Fox, J., & Das, S. (2000). Safe and sound: Artificial intelligence in hazardous applications. Cambridge, MA: MIT Press] and Norman and Shallice’s [Norman, D.A., & Shallice, T. (1986). Attention to action: Willed and automatic control of behaviour. In R. Davidson, G. Schwartz, & D. Shapiro (Eds.), Consciousness and Self Regulation (Vol. 4). New York: Plenum] theory of willed and automatic action. Two strategies and a simple perceptual bias are implemented within the models and comparisons between model and child performance reveal a good fit for the key dependent measures (number of rule breaks and percentage of incomplete solutions) of the two groups

Verbalization and problem solving: insight and spatial factors

Original article can be found at: http://www.bpsjournals.co.uk/ Copyright The British Psychological SocietyTwo groups of participants attempted eight examples of each of four different problem types formed by combining insight v. non-insight and verbal v. spatial factors. The groups were given different verbalization instructions viz., Silent (N=40) or Direct Concurrent (N=40). There were significant differences between insight and non-insight tasks and between spatial and verbal tasks in terms of solution rates and latencies. Significant interactions between the verbal v. spatial factor and verbalization condition on solution rates and latencies reflected a greater (negative) effect of verbalizing on spatial as against verbal problems. However, no significant interactions of the insight v. non-insight factor with verbalization condition on solution rates or latencies were found. These results favoured the “business as usual” view of insight problem solving as against the “special process” view which predicted larger effects of verbalization for insight problems as against non-insight problems.Peer reviewe

Executive functions in insight versus non-insight problem solving: an individual differences approach

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713685607~db=all Copyright Informa / Taylor and FrancisThis study investigated the roles of the executive functions of inhibition and switching and of verbal and visuo-spatial working memory capacities in insight and non-insight tasks. Eighteen insight tasks, 10 non-insight tasks and measures of individual differences in working memory capacities, switching and inhibition were administered to 120 participants. Performance on insight problems was not linked with executive functions of inhibition or switching but was linked positively to measures of verbal and visuo-spatial working memory capacities. Non-insight task performance was positively linked to the executive function of switching (but not to inhibition) and to verbal and visuo-spatial working memory capacities. These patterns regarding executive functions were maintained when the insight and non-insight composites were split into verbal and spatial insight and non-insight composite scores. The results are discussed in relation to dual processing accounts of thinking.Peer reviewe

Graphs, Random Walks, and the Tower of Hanoi

The Tower of Hanoi puzzle with its disks and poles is familiar to students in mathematics and computing. Typically used as a classroom example of the important phenomenon of recursion, the puzzle has also been intensively studied its own right, using graph theory, probability, and other tools. The subject of this paper is “Hanoi graphs”, that is, graphs that portray all the possible arrangements of the puzzle, together with all the possible moves from one arrangement to another. These graphs are not only fascinating in their own right, but they shed considerable light on the nature of the puzzle itself. We will illustrate these graphs for different versions of the puzzle, as well as describe some important properties, such as planarity, of Hanoi graphs. Finally, we will also discuss random walks on Hanoi graphs

On Rearrangement of Items Stored in Stacks

There are $n \ge 2$ stacks, each filled with $d$ items, and one empty stack. Every stack has capacity $d > 0$. A robot arm, in one stack operation (step), may pop one item from the top of a non-empty stack and subsequently push it onto a stack not at capacity. In a {\em labeled} problem, all $nd$ items are distinguishable and are initially randomly scattered in the $n$ stacks. The items must be rearranged using pop-and-pushs so that in the end, the $k^{\rm th}$ stack holds items $(k-1)d +1, \ldots, kd$, in that order, from the top to the bottom for all $1 \le k \le n$. In an {\em unlabeled} problem, the $nd$ items are of $n$ types of $d$ each. The goal is to rearrange items so that items of type $k$ are located in the $k^{\rm th}$ stack for all $1 \le k \le n$. In carrying out the rearrangement, a natural question is to find the least number of required pop-and-pushes. Our main contributions are: (1) an algorithm for restoring the order of $n^2$ items stored in an $n \times n$ table using only $2n$ column and row permutations, and its generalization, and (2) an algorithm with a guaranteed upper bound of $O(nd)$ steps for solving both versions of the stack rearrangement problem when $d \le \lceil cn \rceil$ for arbitrary fixed positive number $c$. In terms of the required number of steps, the labeled and unlabeled version have lower bounds $\Omega(nd + nd{\frac{\log d}{\log n}})$ and $\Omega(nd)$, respectively