Intensional properties of polygraphs

TL;DR

This paper introduces polygraphic programs as a computational model, demonstrating their Turing completeness and characterizing polynomial time computability using polygraphic interpretations.

Contribution

It presents polygraphic programs as a new subclass of polygraphs that can model first-order functional programs and analyzes their computational complexity.

Findings

Polygraphic programs are Turing complete.

Polygraphic interpretations characterize polynomial time functions.

The paper distinguishes between deterministic and non-deterministic polynomial time functions.

Abstract

We present polygraphic programs, a subclass of Albert Burroni's polygraphs, as a computational model, showing how these objects can be seen as first-order functional programs. We prove that the model is Turing complete. We use polygraphic interpretations, a termination proof method introduced by the second author, to characterize polygraphic programs that compute in polynomial time. We conclude with a characterization of polynomial time functions and non-deterministic polynomial time functions.