The Complexity of Data-Free Nfer

2024-07-03

Runtime Verification

AI Summary

This paper investigates the computational complexity of evaluation and satisfiability for data-agnostic Nfer—a runtime verification language for event traces. The evaluation problem asks whether a given input trace entails a specified temporal interval under a rule set; the satisfiability problem asks whether some input trace exists that entails the interval. We establish that evaluation is polynomial-time decidable—first such result for Nfer. For the fragment restricted to inclusion-only rules, we provide a polynomial-time satisfiability decision procedure. We precisely characterize the decidability boundary: satisfiability is decidable for acyclic rule sets but undecidable in general for data-agnostic Nfer. Our analysis integrates formal language theory, interval temporal logic semantics, and complexity-theoretic techniques. The results deliver foundational complexity characterizations and efficient algorithms for event-trace verification, advancing the theoretical underpinnings and practical applicability of runtime monitoring for temporal specifications.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Security and Privacy: Data transparency and provenance

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 and undecidability for satisfiability of full data-free nfer.

Problem

• Analyzing complexity of data-free nfer evaluation problem
• Studying satisfiability problem for interval generation rules
• Establishing decidability bounds for cycle-free nfer specifications

Innovation

• Polynomial-time algorithms for evaluation problem
• Decidability for cycle-free specifications satisfiability
• Undecidability for full data-free nfer satisfiability