多正则函数的Pebble极小化
Pebble Minimization of Polyregular Functions
摘要：
我们表明，一个多正则字到字的功能是经常的，当且仅当其输出大小是在其输入大小的线性。此外，一个多正则函数可以实现：一个传感器与两个卵石当且仅当其输出有二次大小在其输入，一个传感器与三个卵石当且仅当其输出有立方大小在其输入等此外，表征是可判定的，并给出一个多正则函数，可以计算一个传感器实现它的最小数量的卵石。我们将结果应用于从词到词的mso解释。我们发现，mso的解释尺寸k正好符合k-pebble转导。
英文摘要：
We show that a polyregular word-to-word function is regular if and only if its output size is at most linear in its input size. Moreover a polyregular function can be realized by: a transducer with two pebbles if and only if its output has quadratic size in its input, a transducer with three pebbles if and only if its output has cubic size in its input, etc. Moreover the characterization is decidable and, given a polyregular function, one can compute a transducer realizing it with the minimal number of pebbles. We apply the result to mso interpretations from words to words. We show that mso interpretations of dimension k exactly coincide with k-pebble transductions.
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