Many NP-complete problems take integers as part of their input instances. These input integers are generally binarized, that is, provided in the form of the "binary" numeral representation, and the lengths of such binary forms are used as a basis unit to measure the computational complexity of the problems. In sharp contrast, the "unarization" (or the "unary" numeral representation) of numbers has been known to bring a remarkably different effect onto the computational complexity of the problems. When no computational-complexity difference is observed between binarization and unarization of instances, on the contrary, the problems are said to be strong NP-complete. This work attempts to spotlight an issue of how the unarization of instances affects the computational complexity of various combinatorial problems. We present numerous NP-complete (or even NP-hard) problems, which turn out to be easily solvable when input integers are represented in unary. We then discuss the computational complexities of such problems when taking unary-form integer inputs. We hope that a list of such problems signifies the structural differences between strong NP-completeness and non-strong NP-completeness.

翻译：许多NP完全问题将整数作为其输入实例的一部分。这些输入整数通常采用二进制数表示法（即"二进制"数字表示）进行编码，其二进制形式的长度被用作衡量问题计算复杂度的基础单位。与之形成鲜明对比的是，数字的"一元化"（即"一元"数字表示法）已被证明会对问题的计算复杂度产生显著不同的影响。反之，当实例的二进制化与一元化之间未观察到计算复杂度差异时，这类问题被称为强NP完全问题。本文旨在聚焦实例一元化如何影响各类组合问题的计算复杂度这一议题。我们展示了大量NP完全（甚至NP困难）问题，这些问题的输入整数以一元表示时变得易于求解。随后，我们讨论了此类问题在接收一元形式整数输入时的计算复杂度。我们希望这些问题列表能揭示强NP完全性与非强NP完全性之间的结构性差异。