On Measuring Non-Recursive Trade-Offs

TL;DR

This paper provides a theoretical framework for understanding non-recursive trade-offs between descriptional systems, categorizing their growth rates and linking them to language family properties and decision problem decidability.

Contribution

It introduces a general method to deduce bounds on non-recursive trade-offs and offers a qualitative classification based on language theory and decidability criteria.

Findings

Developed bounds on growth rates of non-recursive trade-offs

Identified criteria linking trade-offs to language family closure properties

Classified non-recursive trade-offs qualitatively

Abstract

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems.