The Complexity of Evaluating nfer

TL;DR

This paper analyzes the computational complexity of evaluating the nfer language, revealing undecidability in general and providing efficient algorithms for practical restrictions.

Contribution

It offers the first complexity analysis of nfer evaluation, establishing decidability boundaries and algorithms for practical cases.

Findings

Full nfer evaluation is undecidable due to recursion and infinite data.

Restricting recursion or data domain yields decidable and tight complexity results.

A polynomial-time algorithm is provided for minimality with finite data.

Abstract

Nfer is a rule-based language for abstracting event streams into a hierarchy of intervals with data. Nfer has multiple implementations and has been applied in the analysis of spacecraft telemetry and autonomous vehicle logs. This work provides the first complexity analysis of nfer evaluation, i.e., the problem of deciding whether a given interval is generated by applying rules. We show that the full nfer language is undecidable and that this depends on both recursion in the rules and an infinite data domain. By restricting either or both of those capabilities, we obtain tight decidability results. We also examine the impact on complexity of exclusive rules and minimality. For the most practical case, which is minimality with finite data, we provide a polynomial-time algorithm.