卵石极小化：最后定理
Pebble minimization: the last theorems
摘要：
pebble传感器是嵌套的双向传感器，可以在其输入单词上放置标记（称为"pebbles"）。此类机器可以计算输出大小与输入大小成多项式的函数。它们可以被看作是简单的递归程序，其递归高度是有界的。一个自然的问题是，给定卵石换能器，计算具有最小递归高度的等效卵石换能器。这个问题是开放的，因为该模型的引入。在本文中，我们研究了卵石换能器的两个限制，即不能看到标记（Nguyên等人介绍的"盲卵石换能器"），或者只能看到最后落下的标记（Engelfriet等人介绍的"最后的卵石换能器"）。对于这两种模型，我们提供了一个有效的算法，最小化递归高度。在这两种情况下使用的关键属性是，一个函数的输出大小是线性的（分别为：二次、三次等）总是可以由递归高度为1的机器计算（分别为）。2、3等）。我们最后表明，这个关键属性失败，只要我们考虑机器，可以看到一个以上的标记。
英文摘要：
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Such machines can compute functions whose output size is polynomial in the size of their input. They can be seen as simple recursive programs whose recursion height is bounded. A natural problem is, given a pebble transducer, to compute an equivalent pebble transducer with minimal recursion height. This problem is open since the introduction of the model. In this paper, we study two restrictions of pebble transducers, that cannot see the marks ("blind pebble transducers" introduced by Nguyên et al.), or that can only see the last mark dropped ("last pebble transducers" introduced by Engelfriet et al.). For both models, we provide an effective algorithm for minimizing the recursion height. The key property used in both cases is that a function whose output size is linear (resp. quadratic, cubic, etc.) can always be computed by a machine whose recursion height is 1 (resp. 2, 3, etc.). We finally show that this key property fails as soon as we consider machines that can see more than one mark.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
