Polygraphic programs and polynomial-time functions

TL;DR

This paper introduces polygraphic programs as a formal model for first-order functional programs, demonstrating their Turing-completeness and their capacity to characterize polynomial-time computable functions using algebraic analysis tools.

Contribution

It establishes polygraphic programs as a Turing-complete model and identifies a subclass that precisely captures polynomial-time functions with algebraic complexity analysis.

Findings

Polygraphic programs are Turing-complete.

A subclass computes exactly polynomial-time functions.

Polygraphic interpretations enable complexity analysis.

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.