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
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