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Regular expressions are commonly used for finding and extracting matches from sequence data. Due to the inherent ambiguity of regular expressions, a disambiguation policy must be considered for the match extraction problem, in order to uniquely determine the desired match out of the possibly many matches. The most common disambiguation policies are the POSIX policy and the greedy (PCRE) policy. The POSIX policy chooses the longest match out of the leftmost ones. The greedy policy chooses a leftmost match and further disambiguates using a greedy interpretation of Kleene iteration to match as many times as possible. The choice of disambiguation policy can affect the output of match extraction, which can be an issue for reusing regular expressions across regex engines. In this paper, we introduce and study the notion of disambiguation robustness for regular expressions. A regular expression is robust if its extraction semantics is indifferent to whether the POSIX or greedy disambiguation policy is chosen. This gives rise to a decision problem for regular expressions, which we prove to be PSPACE-complete. We propose a static analysis algorithm for checking the (non-)robustness of regular expressions and two performance optimizations. We have implemented the proposed algorithms and we have shown experimentally that they are practical for analyzing large datasets of regular expressions derived from various application domains. 

We investigate online monitoring algorithms over dense-time and continuous-time signals for properties written in metric temporal logic (MTL). We consider an abstract algebraic semantics based on complete lattices. This semantics includes as special cases the standard Boolean (qualitative) semantics and the widely-used real-valued robustness (quantitative) semantics. Our semantics also extends to truth values that are partially ordered and allows the modeling of uncertainty in satisfaction. We propose a compositional approach for the construction of online monitors that transform exact representations of piecewise constant (dense-time and continuous-time) signals. These monitors are based on a class of infinite-state deterministic signal transducers that (1) are allowed to produce the output signal with some bounded delay relative to the input signal, and (2) do not introduce unbounded variability in the output signal. A key ingredient of our monitoring framework is an efficient algorithm for sliding-window aggregation over dense-time signals. We have implemented and experimentally evaluated our monitoring framework by comparing it to the recently proposed online monitoring tools Reelay and RTAMT.