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Deductive and inductive methods for program synthesis

This research paper discusses the use of deductive and inductive methods for program synthesis, including the use of inductive programming and the application of differential evolution optimization. Experimental data and results are also presented. The research is ongoing, and further testing and expansion of the methodology is required.

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Deductive and inductive methods for program synthesis

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  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. Inductive programming Set of behaviours program Requirements specification algorithm Deductive programming Program construction

  4. y R1 t R6 R2 u z R3 R5 v R4 composition Problem Statement x

  5. IN OUT x1 t1 x2 t2 … … xn tn Scoring of programs s - measure of fitness pi=R1; R2; R3; R4; R5; ... ;R6 Square root fitness measure of the program p

  6. Program synthesis asoptimization s z0 z 1 h P=R2; R3; R5; R6; R2; …; R6

  7. Coding of programs z = 0,23562…7 h p=R2; R3; R5; R6; R2; …; R6

  8. y R1 t R6 x R2 u z R3 R5 v R4 Coding of programs (2) PR6 M(P) - State Transition Machine computational model

  9. Coding of programs (3) z = 0.912 1 0 p=R3; . . .  1 0 p=R3; R4; . . .  P=R3;R4;R1;R5;R6 2 x , 3 1 xy xz 2 , 4 1 3 xyz vxz 5 2 4;5 , 1 4 uvxz vxyz 2 , 1 5 0.33 0.66 uvxyz 4;5 6 tuvxyz

  10. Function to be optimized (f(z)) s 1 z

  11. 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

  12. y R1 t R6 x R2 u z R3 R5 v R4 Experimental Data I(R1)=“y:=ln(x)” I(R2)=“y:=exp(-x)” I(R3)=“z:=x^3+6x” I(R4)=“v:=2(x^2+z)” I(R5)=“(u,z):=(v+6,v/2)” I(R6)=“v:=0.16yu/7.85^4” P={(0.75,1.87*10^-07), (0.70, 1.04*10^-07) (0.65,5.44*10^-08), (0.60,2.61*10^-08) (0.55,1.17*10^-08),(0.50, 3.40*10^-09)} P.M. Murphy and D.W. Aha, Uci repository of machine learning databases

  13. Experimental Data (2) I(R1)=“y:=ln(x)” I(R2)=“y:=exp(-x)” I(R3)=“z:=x^3+6x” I(R4)=“v:=2(x^2+z)” I(R5)=“(u,z):=(v+6,v/2)” I(R6)=“v:=0.16yu/7.85^4” The optimal solutions like 0.37362, 0.40419, 0.795112 correspond to the following sequence of relations “R2;R3;R4;R5;R4;R5;R4;R5;R6” The optimal solution of the problem obtained by the DE method corresponds to the proposed by Knut Angström functional relation: where

  14. 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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