Parametrizing Reads-From Equivalence for Predictive Monitoring

2026-04-07

AI Summary

This work addresses the challenge of predictive runtime monitoring for concurrent programs, which requires balancing expressive power against algorithmic efficiency. The authors propose a k-slice reordering model that partitions an execution trace into \(k+1\) ordered subsequences, yielding a tunable equivalence framework that preserves program order and read-from constraints. This model induces a hierarchy that converges to read-from equivalence as \(k\) increases, thereby enabling the first systematic trade-off between expressiveness and computational cost. By situating the model between read-from equivalence and Mazurkiewicz trace equivalence and leveraging streaming algorithm design, the approach yields constant-space streaming algorithms that efficiently solve the predictive monitoring problem for any fixed \(k\) and regular specification.

Abstract

Predictive runtime monitoring asks whether an execution $σ$ of a concurrent program can be used to \emph{soundly predict} the existence of a reordering $ρ$ of $σ$ that satisfies a property $\varphi$. Its effectiveness and efficiency depend on two factors: (a) the complexity of $\varphi$, and (b) the expressive power of the reorderings considered. At one extreme, allowing all reorderings induced by \emph{reads-from equivalence} makes predictive monitoring intractable, even for simple properties such as data races. At the other extreme, restricting to commutativity-based reorderings (Mazurkiewicz trace equivalence) yields efficient algorithms for simple properties, but remains intractable for general regular specifications and offers limited predictive power. We address this tradeoff via \emph{parametrization}. We introduce \emph{sliced reorderings} and their generalization, \emph{$k$-sliced reorderings}. Informally, $ρ$ is a $k$-sliced reordering of $σ$ if $σ$ can be partitioned into $k+1$ ordered subsequences whose concatenation yields $ρ$, while preserving program order and reads-from constraints. Our results are twofold. First, $k$-sliced reorderings form a strictly increasing hierarchy that converges to reads-from equivalence as $k$ grows. Second, for any fixed $k$, predictive monitoring modulo $k$-sliced reorderings against any regular specification admits a constant-space streaming algorithm. Together, these results establish $k$-sliced reorderings as a principled alternative to existing equivalences, enabling a uniform parametrized framework where expressive power can be systematically traded off against computational cost.

Problem

• predictive monitoring
• concurrent programs
• reads-from equivalence
• reorderings
• runtime verification

Innovation

• k-sliced reorderings
• predictive runtime monitoring
• reads-from equivalence
• parametrized concurrency
• streaming algorithm