Resources and co-resources: a junction between semantics and descriptive complexity

我们生活在一个信息时代，当计算机和驱动它们的软件渗透到我们社会的各个方面时，计算有两个基本的重要方面。一个是执行计算任务所需的资源：需要多少计算步骤，需要多少计算机内存等。另一个是关于我们掌握我们创建和使用的计算机系统的惊人复杂性的能力。管理这种复杂性的唯一方法是使用模块化和抽象的原则，这样在我们设计和构建系统的每一步，我们只看到非常有限的一部分，我们可以掌握其复杂性。虽然随着计算机科学的发展，对计算的每一个方面的研究都有了很大的进步，目前，我们对它们之间的关系了解非常有限。在我们以前工作的基础上，本项目旨在大大加强我们对这些问题的共同理解，并在此基础上开发新的数学工具和方法来研究计算。这反过来又可能导致在该领域取得根本性进展的新的可能性。

We live in an information age, when computers and the software that drives them permeate every aspect of our society.There are two fundamentally important aspects of computation.- One concerns the resources needed to perform computational tasks: how many computational steps are needed, how much computer memory, etc.- The other concerns our ability to master the staggering complexity of the computer systems we create and use. The only way of managing this complexity is to use principles of modularity and abstraction, so that at each step of our design and construction of the system, we see only a very limited piece, whose complexity we can master.While the study of each of these aspects of computing has been greatly advanced as computer science has developed, currently we have a very limited understanding of how they relate to each other.Building on our previous work, this project aims to greatly enhance our common understanding of these issues, and to develop new mathematical tools and methods for studying computation based on this. This can lead in turn to new possibilities for fundamental advances in the field.