---
title: Polygraphic programs and polynomial-time functions
url: https://www.emergentmind.com/papers/0701032
type: paper
arxiv_id: '0701032'
arxiv_url: https://arxiv.org/abs/0701032
published: '2007-01-05'
categories:
- cs.LO
- cs.CC
- math.CT
---

# Polygraphic programs and polynomial-time functions

## Abstract

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a Turing-complete computational model. Their algebraic structure is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turing-computable in polynomial time.