范畴数据类型中的几乎同态问题(英文)

Almost-homomorphism in the categorical data type

范畴数据类型可以看成是抽象数据类型的扩充,它的对象就是封装了数据表达式以及涉及同态操作的控制流的集合。因此同态的关系是构造范畴数据类型关键,但是,在数据类型中有些操作并不是同态操作。本文扩充了范畴数据类型中同态思想,得到了范畴数据类型中几乎同态的理论基础,同时我们通过例子说明了同态方法不能解决的并行计算问题可以用几乎同态的方法来解决。总之,在元组元素的运算上几乎同态问题比同态问题更复杂些,并且它扩充了范畴数据类型变换的应用范围。

Categorical Date Type （CDT） can be regarded as a generalization of abstract data types, whose object is encapsulated data representation and also the control flow involved in evaluating homomorphism. So the relations of homomorphism are key ideas in construction of categorical data types, however there are some functions that are not homomorphism in data types. In this paper, we extend the homomorphism in the categorical data type, and get theoretical basis of the almost-homomorphism in the categorical data type, in the mean time, we use some examples to show the fact when homomorphism cannot be solved in the parallel computation we can use almost-homomorphism instead. In brief, almost-homomorphism is more difficult than homomorphism on the operation of the elements of tuple, and it extends the application area of CDT translation.