to RCF decision procedures

journeycartAI and Robotics

Oct 15, 2013 (3 years and 11 months ago)

117 views

Application of machine learning

to RCF decision procedures

Zongyan Huang

What is MetiTarski


Automatic theorem prover


Prove universally quantified inequalities
involving special functions (ln, exp, sin, etc.,.)


e.g.





Prove within a second!

Why reasoning about

special functions


Wide ranges of engineering applications


Mechanical systems


Electrical circuits


Chemical process control


Embedded computation systems


Hybrid systems are dynamic system which
exhibits both continuous and discrete
dynamic behavior


Properties are expressed by formula
involving special functions


How MetiTarski works


Combines a resolution theorem prover
(Metis) with RCF decision procedures


The theory of RCF concerns boolean
combinations of polynomial equations and
inequalities over the real numbers


Eliminate special functions (upper and lower
bounds)


Transform parts of the problem into
polynomial inequalities


Apply a RCF decision procedure

RCF decision procedures


Proof search generates a series of RCF
subproblems


Simplify clauses by deleting literals that are
inconsistent with other algebraic facts


RCF Strategies used


QEPCAD


Mathematica


Z3


No single RCF decision procedure always
gives the fastest runtime


Use machine learning to find the

best


RCF
strategy




Machine Learning


Statistical methods to infer information from
training examples


Information applied to new problems


The Support Vector Machine (Joachims


SVMLight)


SVM learn: generate model


SVM classify: predict the class label and output the margin
values


Methodology


Identify features of the problems


Select the best kernel function and parameter
values for SVM
-
Light base on
F
1

maximization





Combine the models for decision procedures


Compare the margin values. The classifier with
most positive (or least negative) margin was
selected.


Results


The experiment was done on 825 MetiTarski
problems


The total number of problems proved out of
194 testing problems was used to measure
the efficacy


Machine learned selection yields better results
than any individual fixed decision procedure


Machine learned

Fix Z3

Fix Mathematica

Fix QEPCAD

163

160

153

158

Future work


Extend to the heuristic selection within
decision procedures


Extend the range of features used and
apply feature selection


Provide feedback for development of RCF
decision procedures


Thank you