Formal Systems Laboratory

Generating Optimal Monitors for Extended Regular Expressions

Abstract. Ordinary software engineers and programmers can easily understand regular patterns, as shown by the immense interest in and the success of scripting languages like Perl, based essentially on regular expression pattern matching. We believe that regular expressions provide an elegant and powerful specification language also for {\em monitoring requirements}, because an execution trace of a program is in fact a string of states. Extended regular expressions (EREs) add complementation to regular expressions, which brings additional benefits by allowing one to specify patterns that must {\em not} occur during an execution. Complementation gives one the power to express patterns on strings more compactly. In this paper we present a technique to generate {\em optimal monitors} from EREs. Our monitors are deterministic finite automata (DFA) and our novel contribution is to generate them using a modern coalgebraic technique called {\em coinduction}. Based on experiments with our implementation, which can be publicly tested and used over the web, we believe that our technique is more efficient than the simplistic method based on complementation of automata which can quickly lead to a highly-exponential state explosion.