Tuple Interpretations and Applications to Higher-Order Runtime Complexity

TL;DR

This paper explores tuple interpretations, a flexible algebraic method that generalizes polynomial and matrix interpretations, to analyze the innermost runtime complexity of higher-order term rewriting systems.

Contribution

It adapts tuple interpretations specifically for assessing the innermost runtime complexity in higher-order rewriting systems.

Findings

Tuple interpretations can effectively analyze higher-order TRSs.

The approach provides new insights into innermost runtime complexity.

Potential for improved complexity bounds in higher-order rewriting.

Abstract

Tuple interpretations are a class of algebraic interpretation that subsumes both polynomial and matrix interpretations as it does not impose simple termination and allows non-linear interpretations. It was developed in the context of higher-order rewriting to study derivational complexity of algebraic functional systems. In this short paper, we continue our journey to study the complexity of higher-order TRSs by tailoring tuple interpretations to deal with innermost runtime complexity.