The devil is in Asymmetries (Rough Version)
Edinah K. Gnang, Vidit Nanda
TL;DR
This paper explores how asymmetries in systems of polynomial equations over boolean variables create computational obstacles, affecting the tractability of solving such combinatorial problems.
Contribution
It formally analyzes the impact of asymmetries on the computational complexity of solving polynomial systems in boolean variables.
Findings
Asymmetries significantly influence problem tractability.
Algebraic obstacles are linked to the magnitude of asymmetries.
Understanding asymmetries can guide complexity analysis.
Abstract
We formally investigate some computational obstacles to tractability of computing the variety determined by K complex polynomials in N boolean variables. We show that using algebraic methods for solving combinatorial problems, the obstacles to tractability lies in the order of magnitude of asymmetries admitted by the given system of equations.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Commutative Algebra and Its Applications