Deductive and inductive methods for program synthesis

1
Deductive and inductive methods for program
synthesis

• Jelena Sanko, Jaan Penjam
• Institute of Cybernetics

October 29, 2005
2
Agenda

• Program construction
• Inductive program construction
• Experiments
• Conclusions

3
Program construction
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Problem Statement
x
5
Scoring of programs
s - measure of fitness
pi?R1 R2 R3 R4 R5 ... R6?
Square root fitness measure of the program p
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Program synthesis as optimization
s
z0
z
1
h
P?R2 R3 R5 R6 R2 R6?
7
Coding of programs
z 0,235627
h
p?R2 R3 R5 R6 R2 R6?
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PR6
Coding of programs (2)
M(P) - State Transition Machine
computational model
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Coding of programs (3)
2
x
,
3
1
xy
xz
2
4
,
1
3
xyz
vxz
5
45
2
,
1
4
uvxz
vxyz
2
,
1
5
0.33
0.66
uvxyz
45
6
tuvxyz
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Function to be optimized (f(z))
s
1
z
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Optimization technique
-Differential Evolution,
Rainer Storn and Kenneth Price
DE is a method for finding extreme points of
real-valued multi-modal functions
DE is a heuristic method that can be used for
optimization of non-differentiable functions in
continuous spaces
The convergence rate of the floating-point
encoded DE is more than 10 times higher than the
convergence rate of the traditional binary
encoded GA
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Experimental Data
I(R1)yln(x) I(R2)yexp(-x) I(R3)zx3
6x I(R4)v2(x2z) I(R5)(u,z)(v6,v/2) I
(R6)v0.16yu/7.854
P(0.75,1.8710-07), (0.70, 1.0410-07) (0.65,5
.4410-08), (0.60,2.6110-08) (0.55,1.1710-08)
,(0.50, 3.4010-09)
P.M. Murphy and D.W. Aha, Uci repository of
machine learning databases
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Experimental Data (2)
I(R1)yln(x) I(R2)yexp(-x) I(R3)zx3
6x I(R4)v2(x2z) I(R5)(u,z)(v6,v/2) I
(R6)v0.16yu/7.854
The optimal solutions like 0.37362, 0.40419,
0.795112 correspond to the following sequence
of relations R2R3R4R5R4R5R4R5R6
The optimal solution of the problem obtained by
the DE method corresponds to the proposed by Knut
Angström functional relation
where
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Conclusions

• The inductive approach to program construction
  can promote control over construction process and
  take an appropriate decision when several
  solutions are available
• IPS uses interpretation of relations and a
  fitting function
• IPS considers all programs and selects the best
• The research is in progress...
• IPS strategy need to be checked in practice and
  extension to high order constraints is required

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