有界图灵机的对称性和转移
Symmetries and transitions of bounded Turing machines
摘要：
我们考虑的结构，通过反复推广有限状态自动机的定义的对称性考虑，并在每一步构建类似的过渡幺半群。这种方法首先给我们非确定性自动机，然后（非确定性）双向自动机和有界图灵机-也就是说，读/写头不能移动超过输入字的结尾的图灵机。在双向自动机的情况下，过渡幺半群推广到紧闭范畴中的自同态幺半群。这些使用Girard的分辨率公式（来自线性逻辑的相互作用几何表示）来构建单例词的图像。在有界图灵机的情况下，过渡同态推广到从自然数到由紧闭范畴的自同态幺半群的并集构造的幺半群的幺半群同态，以及适当的合成。它们使用Girard的执行公式（也来自线性逻辑的交互作用几何表示）来构造单例的图像。
英文摘要：
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic automata, then (non-deterministic) two-way automata and bounded Turing machines --- that is, Turing machines where the read / write head is unable to move past the end of the input word. In the case of two-way automata, the transition monoids generalise to endomorphism monoids in compact closed categories. These use Girard's resolution formula (from the Geometry of Interaction representation of linear logic) to construct the images of singleton words. In the case of bounded Turing machines, the transition homomorphism generalises to a monoid homomorphism from the natural numbers to a monoid constructed from the union of endomorphism monoids of a compact closed category, together with an appropriate composition. These use Girard's execution formula (also from the Geometry of Interaction representation of linear logic) to construct images of singletons.
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