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Rewriting Structured Cospans: A Syntax for Open Systems

  • Author(s): Cicala, Daniel Michael
  • Advisor(s): Baez, John
  • et al.
Creative Commons 'BY' version 4.0 license
Abstract

The concept of a system has proliferated through natural

and social sciences. While myriad theories of systems

exist, there is no mathematical general theory of

systems. In this thesis, we take a first step towards

formulating such a theory. Our focus is on developing a

syntax for compositional systems equipped with a rewriting

theory. We pull from category theory and linguistics to

accomplish this. The basic syntactical unit is a

structured cospan and rewriting is introduced via the

double pushout method. Two versions of rewriting are

proposed: one that tracks intermediate steps and another

disregards them. Benefits and drawbacks of both versions

are discussed. We apply our results to the decomposition

of closed systems, obtaining a structurally inductive

viewpoint of rewriting such systems.

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