Transcript slides

Implications of the
Tower of Hanoi Problem for
ACT-R’s Goal Stack
John R. Anderson
Scott Douglass
Psychology Department
Carnegie Mellon University
Pittsburgh, PA 15213
[email protected]
ACT-R Home Page:
http://act.psy.cmu.edu
Fig u r e 2 .3 Fiv e - d is k To w e r o f Ha n o i P r o b le m s
Ruiz’s Data
5.0
Data
Theory
Latency (Sec.)
4.0
3.0
2.0
1.0
0.0
0
4
8
12 16 20 24
Move Number
28
32
Random 4-Disk Problems
Anderson, Kushmerick & Lebiere (1993)
10.0
Data
Theory
9.0
8.0
Latency
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Move Number
Posted Steps for a 3-4-2 Problem
Push
Push
Push
Move
Move
Move
Move
Push
Move
Move
Move
Move
Push
Move
Move
Move
4-disk to Peg C
3-disk to Peg A
2-disk to Peg B
1-disk to Peg A
2-disk to Peg B
1-disk to Peg B
3-disk to Peg A
2-disk to Peg A
1-disk to Peg C
2-disk to Peg A
1-disk to Peg A
4-disk to Peg C
2-disk to Peg C
1-disk to Peg B
2-disk to Peg C
1-disk to Peg A
Experimental Design
7 problems 3 times for each of 3 days
eye movements tracked
4-5-4 -- 31 moves, 15 subgoals
4-5-3 -- 23 moves, 11 subgoals
3-5-4 -- 23 moves, 11 subgoals
3-5-3 -- 15 moves, 7 subgoals
3-4-3 -- 15 moves, 7 subgoals
3-4-2 -- 11 moves, 5 subgoals
2-4-3 -- 11 moves, 5 subgoals
3 tower after pushing 4
Accuracy on a 3-4-2 Problem
Latency on 3-4-2 Problems
Accuracy on 3-Disk Subsequence
Error Distribution on
3-Disk Subsequence
Goal Fixations on 3-Disk Subsequence
Latency on 3-Disk Subsequence
After Pushing 4-Disk
Latency on 3-Disk Subsequence
to End Problem
3 at End
1750
1500
Disk
1250
Peg
1000
Action
750
500
Step
Latency on 3-Disk Subsequence
Under a 5-Disk
3 under 5
1750
1500
Disk
1250
Peg
1000
Series3
750
500
Step
Production Rules for Pushing and Popping
Without a Goal Stack
(p Subgoal-Blocker
=goal>
isa do-tower
check-loc =loc1
spare =loc2
- spare =loc1
check =size
success failure
!eval! (> =size 1)
==>
=goal>
check-loc nil
=newgoal>
isa do-tower
p-disk =size
p-from =loc1
p-to =loc2
parent =goal
check (!eval! (1- =size))
spare (!eval! (other-disk =loc2 =loc1))
check-loc (!eval! (encode-problem (1- =size)))
!focus-on! =newgoal)
(p Retrieve-Parent
=goal>
isa do-tower
p-disk =disk
success t
parent =parent
=parent>
isa do-tower
!eval! (> *stack* 0)
==>
!focus-on! =parent)
(p Move-disk-1-2
=goal>
isa do-tower
check 1
disk 2
success failure
check-loc =p
p-from =q
p-to =r
!eval! (or (equal =p =q) (equal =p =r))
==>
!output! 1
=goal>
success peg
check skip)
Simulated Error Rates (and Data) for
3-Disk Subsequences
1.000
0.900
0.800
0.700
0.600
0.500
Step
Simulated Latencies (and Data)
for 3-Disk Subsequences