Observation of implicit complexity by non confluence

TL;DR

This paper investigates how non confluence affects the implicit computational complexity of certain classes of first-order functional programs, revealing complexity class separations linked to their intentional properties.

Contribution

It demonstrates that introducing non confluence into well-known PTIME classes results in NPTIME and PSPACE complexities, highlighting the connection between confluence properties and computational complexity.

Findings

Adding non confluence to cons-free programs yields PTIME to NPTIME jump.

Non confluence in programs with interpretations leads to PSPACE complexity.

Separation of classes reflects their underlying intentional properties.

Abstract

We propose to consider non confluence with respect to implicit complexity. We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of cons-free programs, the class of programs with an interpretation, and the class of programs with a quasi-interpretation together with a termination proof by the product path ordering. They all correspond to PTIME. We prove that adding non confluence to the rules leads to respectively PTIME, NPTIME and PSPACE. Our thesis is that the separation of the classes is actually a witness of the intentional properties of the initial classes of programs.