On the Construction of Monitors for Temporal Logic Properties

Abstract Temporal logic is a valuable tool for specifying correctness properties of reactive programs. With the advent of temporal logic model checkers, it has become an important aid for the verification of concurrent and reactive systems. In model checking the temporal logic properties are verified against models expressed in the tool's modelling language. In addition, model-checking techniques are useful to test actual implementations or to verify models of the system that are too detailed to be analysed by a model checker, by means of, for instance, simulation. A tableau construction is an algorithm that translates a temporal logic formula into a finite-state automaton that accepts precisely all the models of the formula. It is a key ingredient to checking satisfiability of a formula as well as to the automata-theoretic approach to model checking. An improvement to the efficiency of tableau constructions has been the development of on-the-fly versions. In this paper, we present a particular tableau construction for the incremental analysis of execution traces during test, simulation or model-checking. The automaton forms the basis of a monitor that detects both good and bad prefix of a particular kind, namely those that are informative for the property under investigation. We elaborate on the construction of the monitor and demonstrate its correctness.