Abstract Runtime predictive analyses enhance coverage of traditional dynamic analyses based bug detection techniques by identifying a space of feasible reorderings of the observed execution and determining if any reordering in this space witnesses the violation of some desired safety property. The most popular approach for modelling the space of feasible reorderings is through Mazurkiewicz’s trace equivalence. The simplicity of the framework also gives rise to efficient predictive analyses, and has been the de facto means for obtaining space and time efficient algorithms for monitoring concurrent programs. In this work, we investigate how to enhance the predictive power of trace-based reasoning, while still retaining the algorithmic benefits it offers. Towards this, we extend trace theory by naturally embedding a class of prefixes, which we call strong trace prefixes. We formally characterize strong trace prefixes using an enhanced dependence relation, study its predictive power and establish a tight connection to the previously proposed notion of synchronization-preserving correct reorderings developed in the context of data race and deadlock prediction. We then show that despite the enhanced predictive power, strong trace prefixes continue to enjoy the algorithmic benefits of Mazurkiewicz traces in the context of prediction against co-safety properties, and derive new algorithms for synchronization-preserving data races and deadlocks with better asymptotic space and time usage. We also show that strong trace prefixes can capture more violations of pattern languages. We implement our proposed algorithms and our evaluation confirms the practical utility of reasoning based on strong prefix traces.

Array-based encodings of tree structures are often preferable to linked or abstract data type-based representations for efficiency reasons. Compared to the more traditional encodings, array-based trees do not immediately offer convenient induction principles, and the programs that manipulate them often implement traversals non-recursively, requiring complex loop invariants for their correctness proofs.

While current bug detection techniques for concurrent software focus on unearthing low-level issues such as data races or deadlocks, they often fall short of discovering more intricate temporal behaviours that can arise even in the absence of such low-level issues. In this paper, we focus on the problem of dynamically analysing concurrent software against high-level temporal specifications such as LTL. Existing techniques for runtime monitoring against such specifications are primarily designed for sequential software and remain inadequate in the presence of concurrency — violations may be observed only in intricate thread interleavings, requiring many re-runs of the underlying software in conjunction with the analysis. Towards this, we study the problem of predictive runtime monitoring , inspired by the analogous problem of predictive data race detection studied extensively recently. The predictive runtime monitoring question asks, given an execution σ , if it can be soundly reordered to expose violations of a specification. In general, this problem may become easily intractable when either the specifications or the notion of reorderings used is complex. In this paper, we focus on specifications that are given in regular languages. Our notion of reorderings is trace equivalence , where an execution is considered a reordering of another if it can be obtained from the latter by successively commuting adjacent independent actions. We first show that, even in this simplistic setting, the problem of predictive monitoring admits a super-linear lower bound of O ( n α ) , where n is the number of events in the execution, and α is a parameter describing the degree of commutativity, and typically corresponds to the number of threads in the execution. As a result, predictive runtime monitoring even in this setting is unlikely to be efficiently solvable, unlike in the non-predictive setting where the problem can be checked using a deterministic finite automaton (and thus, a constant-space streaming linear-time algorithm). Towards this, we identify a sub-class of regular languages, called pattern languages (and their extension generalized pattern languages ). Pattern languages can naturally express specific ordering of some number of (labelled) events, and have been inspired by popular empirical hypotheses underlying many concurrency bug detection approaches such as the “small bug depth” hypothesis. More importantly, we show that for pattern (and generalized pattern) languages, the predictive monitoring problem can be solved using a constant-space streaming linear-time algorithm. We implement and evaluate our algorithm PatternTrack on benchmarks from the literature and show that it is effective in monitoring large-scale applications.