关于可逆换能器
On Reversible Transducers
摘要：
确定性双向换能器定义了正则函数的鲁棒类，除了其他良好的特性之外，该函数在组合下是封闭的。然而，用于构成双路换能器的最知名的算法导致输入的大小的双指数放大。在本文中，我们介绍了一类传感器的组成具有多项式复杂性。它是一类可逆换能器，其计算步骤可以确定性地反转。虽然在单向设置这个类是不是很有表现力，我们证明了任何双向换能器可以通过一个单一的指数爆破可逆。因此，我们证明了双向换能器的组成可以用一个单一的指数爆破的状态数。一个关系的一致化是一个具有相同定义域的函数，它包含在原始关系中。我们的主要结果实际上表明，我们可以均匀化任何非确定性的双向换能器的可逆换能器与一个单一的指数爆破，提高了已知的结果de Souza，其中有一个四倍指数的复杂性。作为一个侧面的结果，我们的建设也给出了一个二次变换从无拷贝流串换能器双向换能器，提高了指数前界。
英文摘要：
Deterministic two-way transducers define the robust class of regular functions which is, among other good properties, closed under composition. However, the best known algorithms for composing two-way transducers cause a double exponential blow-up in the size of the inputs. In this paper, we introduce a class of transducers for which the composition has polynomial complexity. It is the class of reversible transducers, for which the computation steps can be reversed deterministically. While in the one-way setting this class is not very expressive, we prove that any two-way transducer can be made reversible through a single exponential blow-up. As a consequence, we prove that the composition of two-way transducers can be done with a single exponential blow-up in the number of states. A uniformization of a relation is a function with the same domain and which is included in the original relation. Our main result actually states that we can uniformize any non-deterministic two-way transducer by a reversible transducer with a single exponential blow-up, improving the known result by de Souza which has a quadruple exponential complexity. As a side result, our construction also gives a quadratic transformation from copyless streaming string transducers to two-way transducers, improving the exponential previous bound.
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