The Complexity of Data-Free Nfer

TL;DR

This paper analyzes the computational complexity of data-free Nfer, a runtime verification language, revealing polynomial-time algorithms for certain problems and undecidability in the general case.

Contribution

It provides complexity results for evaluation and satisfiability problems in data-free Nfer, including polynomial-time algorithms and undecidability proofs.

Findings

Polynomial-time algorithms for evaluation and satisfiability with inclusive rules.

Decidability of satisfiability for cycle-free specifications with NExpTime lower bound.

Undecidability of satisfiability for full data-free Nfer.

Abstract

Nfer is a Runtime Verification language for the analysis of event traces that applies rules to create hierarchies of time intervals. This work examines the complexity of the evaluation and satisfiability problems for the data-free fragment of nfer. The evaluation problem asks whether a given interval is generated by applying rules to a known input, while the satisfiability problem asks if an input exists that will generate a given interval. By excluding data from the language, we obtain polynomial-time algorithms for the evaluation problem and for satisfiability when only considering inclusive rules. Furthermore, we show decidability for the satisfiability problem for cycle-free specifications with a NExpTime lower bound and undecidability for satisfiability of full data-free nfer.