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Application of machine learning to RCF decision procedures

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.

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Application of machine learning to RCF decision procedures

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  1. Application of machine learning to RCF decision procedures Zongyan Huang

  2. What is MetiTarski • Automatic theorem prover • Prove universally quantified inequalities involving special functions (ln, exp, sin, etc.,.) e.g. Prove within a second!

  3. 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

  4. 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

  5. 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

  6. 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

  7. Methodology • Identify features of the problems • Select the best kernel function and parameter values for SVM-Light base on F1maximization • Combine the models for decision procedures • Compare the margin values. The classifier with most positive (or least negative) margin was selected.

  8. 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

  9. 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

  10. Thank you

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