التفاصيل البيبلوغرافية
| العنوان: |
Hard to Detect Factors of Univariate Integer Polynomials |
| المؤلفون: |
Dennunzio, Alberto, Formenti, Enrico, Margara, Luciano |
| سنة النشر: |
2022 |
| المجموعة: |
Computer Science |
| مصطلحات موضوعية: |
Computer Science - Computational Complexity |
| الوصف: |
We investigate the computational complexity of deciding whether a given univariate integer polynomial p(x) has a factor q(x) satisfying specific additional constraints. When the only constraint imposed on q(x) is to have a degree smaller than the degree of p(x) and greater than zero, the problem is equivalent to testing the irreducibility of p(x) and then it is solvable in polynomial time. We prove that deciding whether a given monic univariate integer polynomial has factors satisfying additional properties may lead to NP-complete problems in the strong sense. In particular, given any constant value k in Z, we prove that it is NP-complete in the strong sense to detect the existence of a factor that returns a prescribed value when evaluated at x=k or to detect the existence of a pair of factors - whose product is equal to the original polynomial - that return the same value when evaluated at x=k. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2210.07030 |
| رقم الانضمام: |
edsarx.2210.07030 |
| قاعدة البيانات: |
arXiv |