A decidable timeout-based extension of linear temporal logic

Abstract

We develop a timeout extension of propositional linear temporal logic (which we call ToLTL) to specify timing properties of timeout-based models of real-time systems. A timeout is used to model the execution of an action marking the end of a delay. With a view to expressing such timeout constraints, ToLTL uses a dynamic variable to abstract the timeout behaviour in addition to a variable which captures the global clock and some static timing variables which record time instances when discrete events occur. We propose a corresponding timeout tableau for satisfiability checking of the ToLTL formulas. Further we prove that the validity checking for such an extended logic remains PSPACE-complete. Under discrete time semantics, with bounded timeout increments, the model-checking problem which verifies if a ToLTL-formula holds in a timeout Kripke structure is also shown to be PSPACE complete. We further prove that ToLTL, when interpreted over discrete time, can be embedded in the monadic second-order logic with time and timeout and show an expressive completeness result for ToLTL. However, when ToLTL is interpreted over dense time without non-zenoness, the resulting logic becomes -complete (i.e., highly undecidable).