CAJ | 학술논문

平面曲线是指单位闭区间在连续函数映射下的影像。这样的函数叫做曲线的参数化。如果一条曲线有一个单调的参数化函数，该曲线是简单曲线。如果一条曲线有可计算的参数化函数，则相应的曲线是可计算的。Gu、LutzHMayordomo最近证明了，有些可计算的简单曲线没有可计算的参数化函数。这样的曲线叫做强迫折返的。本文探讨的是强迫折返的次数对曲线复杂性的影响。
평면곡선시지단위폐구간재련속함수영사하적영상。저양적함수규주곡선적삼수화。여과일조곡선유일개단조적삼수화함수，해곡선시간단곡선。여과일조곡선유가계산적삼수화함수，칙상응적곡선시가계산적。Gu、LutzHMayordomo최근증명료，유사가계산적간단곡선몰유가계산적삼수화함수。저양적곡선규주강박절반적。본문탐토적시강박절반적차수대곡선복잡성적영향。
A planar curve can be defined as the image of the unit interval under a continuous function which is so-called parametrizafion of the curve. The curves parameterized by injective continuous functions are called simple. If a curve has a computable parametrization, then it is called computable. Surprisingly, Gu, Lutz and Mayordomo show in [4] that there exists a computable simple curve which does not have any injective computable parametrization. That is, the computable parametrization of this curve must retrace the curve. In this paper, we first introduce different classes of computable curves according to the number of retracing allowed in a computable parametrization, then we show an infinite proper hierarchy of these classes. Therefore, the retracing number allowed in the computable parametrization can be used to measure the complexity of a computable curve.