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.

Efficient exact paths for dyck and semi-dyck labeled path reachability (extended abstract)

“…Bradford [20] gives a solution to a quickest-path problem for context-free grammars applied to cryptographic routing. Bradford and Choppella [21] use a special-case of Nykänen and Ukkonen's sign-closure algorithm for DAGs with initial edge costs from {−1, +1}, see also Khamespanah, Khosravi, and Sirjani [22]. Further Bradford and Choppella [21] find actual minimum-cost pointto-point Dyck paths in DAGs.…”

“…Khamespanah, Khosravi, and Sirjani [22] use Nykänen and Ukkonen [2]'s exact path algorithm to improve their model checking algorithms for timed actors in distributed systems. They apply the pseudo-polynomial algorithm's O(n 2 ) path relaxation cost, while accepting the pre-processing costs of O(n 3 ).…”