Efficient TCTL Model Checking Algorithm for Timed Actors

Abstract

Non-Polynomial time complexity of model checking algorithms for TCTL properties in dense time is one of the obstacles against using model checking for timed systems. Alternatively, polynomial time algorithms are suggested for model checking discrete time models presented as Duration Time Graphs (DTG) versus a subset of TCTL formula (TCTL≤,≥). While TCTL≤,≥ can be model checked in polynomial time, the problem of model checking for exact time condition (TCTL=) is an NP-Hard problem unless certain conditions hold. In this work we tackle model checking of timed actors using DTG. At the first step, we propose a reduction technique by folding all the instantaneous transitions, resulting folded timed transition system (FTS). At the second step, we show how the FTS of timed actors with discrete time can be mapped to a DTG. Then, we show when the necessary conditions hold for the FTS of timed actors and hence there is an O(|S|2 • Φ) algorithm for model checking of complete TCTL properties (including TCTL≤,≥ and TCTL=) which have small constant time quantifiers. We use a set of case studies to illustrate the impact of using this technique in different application domains.