# to RCF decision procedures

AI and Robotics

Oct 15, 2013 (4 years and 7 months ago)

122 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!

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

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

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