تقرير
Uniform, Integral and Feasible Proofs for the Determinant Identities
| العنوان: | Uniform, Integral and Feasible Proofs for the Determinant Identities |
|---|---|
| المؤلفون: | Tzameret, Iddo, Cook, Stephen A. |
| سنة النشر: | 2018 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Computer Science - Computational Complexity, Computer Science - Logic in Computer Science, Mathematics - Logic, 03F20, 68Q17, 68Q15, 03F30, F.2.2, F.4.1 |
| الوصف: | Aiming to provide weak as possible axiomatic assumptions in which one can develop basic linear algebra, we give a uniform and integral version of the short propositional proofs for the determinant identities demonstrated over $GF(2)$ in Hrubes-Tzameret [SICOMP'15]. Specifically, we show that the multiplicativity of the determinant function and the Cayley-Hamilton theorem over the integers are provable in the bounded arithmetic theory $\mathbf{VNC}^2$; the latter is a first-order theory corresponding to the complexity class $\mathbf{NC}^2$ consisting of problems solvable by uniform families of polynomial-size circuits and $O(\log ^2 n)$-depth. This also establishes the existence of uniform polynomial-size $\mathbf{NC}^2$-Frege proofs of the basic determinant identities over the integers (previous propositional proofs hold only over the two element field). Comment: 76 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1811.04313 |
| رقم الأكسشن: | edsarx.1811.04313 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |