Extracting Linear Relations from Gröbner Bases for Formal Verification of And-Inverter Graphs
Résumé
Formal verification techniques based on computer algebra have
proven highly effective for circuit verification.
The circuit, given as an and-inverter graph, is encoded using
polynomials that automatically generate a Gröbner
basis with respect to a lexicographic term ordering.
Correctness of the circuit is derived by computing the
polynomial remainder of the specification.
However, the main obstacle is the monomial blow-up
during the reduction, as the degree can increase.
In this paper, we investigate an orthogonal approach and focus the
computational effort on rewriting the Gröbner basis itself. Our goal
is to ensure the basis contains linear polynomials that can be
effectively used to rewrite the linearized specification. We first
prove the soundness and completeness of this technique and then
demonstrate its practical application. Our implementation of this
method shows promising results on benchmarks related to multiplier
verification.
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