Programming low-level controls for knitting machines is a meticulous, time-consuming task that demands specialized expertise. Recently, there has been a shift towards automatically generating low-level knitting machine programs from high-level knit representations that describe knit objects in a more intuitive, user-friendly way. Current high-level systems trade off expressivity for ease-of-use, requiring ad-hoc trapdoors to access the full space of machine capabilities, or eschewing completeness in the name of utility. Thus, advanced techniques either require ad-hoc extensions from domain experts, or are entirely unsupported. Furthermore, errors may emerge during the compilation from knit object representations to machine instructions. While the generated program may describe a valid machine control sequence, the fabricated object is topologically different from the specified input, with little recourse for understanding and fixing the issue. To address these limitations, we introduce instruction graphs , an intermediate representation capable of capturing the full range of machine knitting programs. We define a semantic mapping from instruction graphs to fenced tangles, which make them compatible with the established formal semantics for machine knitting instructions. We establish a semantics-preserving bijection between machine knittable instruction graphs and knit programs that proves three properties - upward, forward, and ordered (UFO) - are both necessary and sufficient to ensure the existence of a machine knitting program that can fabricate the fenced tangle denoted by the graph. As a proof-of-concept, we implement an instruction graph editor and compiler that allows a user to transform an instruction graph into UFO presentation and then compile it to a machine program, all while maintaining semantic equivalence. In addition, we use the UFO properties to more precisely characterize the limitations of existing compilers. This work lays the groundwork for more expressive and reliable automated knitting machine programming systems by providing a formal characterization of machine knittability.

中文翻译：

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UFO 指令图是可机器编织的


对针织机的低级控制进行编程是一项细致、耗时的任务，需要专业知识。最近，人们开始从高级针织表示自动生成低级针织机程序，以更直观、用户友好的方式描述针织对象。当前的高级系统在易用性之间进行权衡，需要临时的活板门来访问机器的全部功能空间，或者以实用性的名义回避完整性。因此，高级技术要么需要领域专家的临时扩展，要么完全不受支持。此外，在编译过程中可能会出现从 knit 对象表示到 machine 指令的错误。虽然生成的程序可以描述有效的机器控制序列，但制造的对象在拓扑上与指定的输入不同，几乎没有办法来理解和解决问题。为了解决这些限制，我们引入了 指令图 ，一种能够捕获所有机器编织程序的中间表示。我们定义了从指令图到围栏缠结的语义映射，这使得它们与机器编织指令的既定形式语义兼容。我们在机器编织指令图和编织程序之间建立了语义保留的二射，证明了三个属性 - 向上、向前和有序 （UFO） - 对于确保存在可以制造图表示的围栏缠结的机器编织程序是必要和足够的。 作为概念验证，我们实现了一个指令图编辑器和编译器，允许用户将指令图转换为 UFO 表示，然后将其编译为机器程序，同时保持语义等效性。此外，我们使用 UFO 属性来更精确地描述现有编译器的局限性。这项工作通过提供机器针织性的正式特征，为更具表现力和可靠的自动化针织机编程系统奠定了基础。