Parametrizing Reads-From Equivalence for Predictive Monitoring
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914455888068608 |
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| author | Farzan, Azadeh Mathur, Umang |
| author_facet | Farzan, Azadeh Mathur, Umang |
| contents | 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 $φ$.
Its effectiveness and efficiency depend on two factors: (a) the complexity of $φ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06533 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametrizing Reads-From Equivalence for Predictive Monitoring Farzan, Azadeh Mathur, Umang Programming Languages Formal Languages and Automata Theory Logic in Computer Science 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 $φ$. Its effectiveness and efficiency depend on two factors: (a) the complexity of $φ$, 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. |
| title | Parametrizing Reads-From Equivalence for Predictive Monitoring |
| topic | Programming Languages Formal Languages and Automata Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2604.06533 |