Hyper pattern matching

2025-07-16

AI Summary

Traditional runtime verification relies on intra-sequence pattern matching, which is inadequate for detecting violations of hyperproperties—such as robustness and non-interference—that require evidence spanning multiple input sequences or disjoint segments of a single sequence. This paper introduces *hyperpattern matching*, the first approach to extend pattern matching to joint analysis across multiple sequences. We formalize hyperpatterns using *nondeterministic asynchronous automata* (NAA) and propose both a baseline algorithm and several heuristic optimizations to improve efficiency. Although the problem is NP-complete, our implementation—HypPAu—demonstrates strong scalability with respect to sequence length, log size, and dimensionality across diverse case studies. HypPAu significantly enhances both the precision of violation localization and the expressiveness of captured evidence, enabling effective detection and diagnosis of hyperproperty violations in practical runtime verification settings.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning
• Search and Optimization: Heuristic Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In runtime verification, pattern matching, which searches for occurrences of a specific pattern within a word, provides more information than a simple violation detection of the monitored property, by locating concrete evidence of the violation. However, witnessing violations of some properties, particularly hyperproperties, requires evidence across multiple input words or different parts of the same word, which goes beyond the scope of conventional pattern matching. We propose here hyper pattern matching, a generalization of pattern matching over a set of words. Properties of interest include robustness and (non-)interference. As a formalism for patterns, we use nondeterministic asynchronous finite automata (NAAs). We first provide a naive algorithm for hyper pattern matching and then devise several heuristics for better efficiency. Although we prove the NP-completeness of the problem, our implementation HypPAu is able to address several case studies scalable in the length, number of words (or logs) and number of dimensions, suggesting the practical relevance of our approach.

Problem

• Extends pattern matching to multiple words for hyperproperties
• Addresses NP-complete complexity with efficient heuristics
• Validates scalability in length, word count, and dimensions

Innovation

• Generalizes pattern matching over multiple words
• Uses nondeterministic asynchronous finite automata
• Implements efficient heuristics for scalability