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Related Experiment Video

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A Decision Procedure for Univariate Polynomial Systems Based on Root Counting and Interval Subdivision.

Anthony Narkawicz¹, Cesar Munoz¹, Aaron Dutle¹

¹NASA Langley Research Center, Hampton, VA 23681-2199.

Journal of Formalized Reasoning

|September 20, 2019

Summary

This study introduces a verified method for solving polynomial systems on the real line. It uses interval subdivision and Sturm

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Area of Science:

Computer Science
Computational Mathematics
Symbolic Computation

Background:

Determining the satisfiability of polynomial systems is a fundamental problem in mathematics and computer science.
Existing methods may lack formal verification or struggle with efficiency for complex systems.

Purpose of the Study:

To present a formally verified decision procedure for univariate polynomial relations over real numbers.
To develop a robust and reliable method for automated reasoning about polynomial systems.

Main Methods:

Combines a root counting function based on Sturm's theorem with an interval subdivision algorithm.
Progressively subdivides the real interval until satisfiability can be determined on subintervals.
Formal verification performed using the Prototype Verification System (PVS).

Main Results:

A decision procedure for determining satisfiability of univariate polynomial systems over the real line.
The procedure is formally verified for soundness within the PVS framework.
A proof-producing strategy for automated theorem proving on polynomial systems was defined.

Conclusions:

The developed decision procedure offers a formally verified and reliable approach to solving polynomial systems.
The integration with PVS enables automated proofs for existential and universal statements.
This work contributes to the field of automated reasoning and symbolic computation.