Hyper pattern matching

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.