Growth in system complexity increases the need for automated techniques dedicated to different log analysis tasks such as Log-based Anomaly Detection (LAD). The latter has been widely addressed in the literature, mostly by means of a variety of deep learning techniques. However, despite their many advantages, that focus on deep learning techniques is somewhat arbitrary as traditional Machine Learning (ML) techniques may perform well in many cases, depending on the context and datasets. In the same vein, semi-supervised techniques deserve the same attention as supervised techniques since the former have clear practical advantages. Further, current evaluations mostly rely on the assessment of detection accuracy. However, this is not enough to decide whether or not a specific ML technique is suitable to address the LAD problem in a given context. Other aspects to consider include training and prediction times as well as the sensitivity to hyperparameter tuning, which in practice matters to engineers. In this paper, we present a comprehensive empirical study, in which we evaluate a wide array of supervised and semi-supervised, traditional and deep ML techniques w.r.t. four evaluation criteria: detection accuracy, time performance, sensitivity of detection accuracy and time performance to hyperparameter tuning. Our goal is to provide much stronger and comprehensive evidence regarding the relative advantages and drawbacks of alternative techniques for LAD. The experimental results show that supervised traditional and deep ML techniques fare similarly in terms of their detection accuracy and prediction time on most of the benchmark datasets considered in our study. Moreover, overall, sensitivity analysis to hyperparameter tuning with respect to detection accuracy shows that supervised traditional ML techniques are less sensitive than deep learning techniques. Further, semi-supervised techniques yield significantly worse detection accuracy than supervised techniques.

Zero-knowledge (ZK) protocols enable software developers to provide proofs of their programs’ correctness to other parties without revealing the programs themselves. Regular expressions are pervasive in real-world software, and zero-knowledge protocols have been developed in the past for the problem of checking whether an individual string appears in the language of a regular expression, but no existing protocol addresses the more complex PSPACE-complete problem of proving that two regular expressions are equivalent. We introduce Crêpe , the first ZK protocol for encoding regular expression equivalence proofs and also the first ZK protocol to target a PSPACE-complete problem. Crêpe uses a custom calculus of proof rules based on regular expression derivatives and coinduction, and we introduce a sound and complete algorithm for generating proofs in our format. We test Crêpe on a suite of hundreds of regular expression equivalence proofs. Crêpe can validate large proofs in only a few seconds each.