Symbolic Verification of Complex Real-time Systems with Clock-restriction Diagram

Abstract

Keywords:Real-world real-time systems may involve many complex structures, which are difficult to verify. We experiment with the model-checking of an applicationlayer html-based web-camera which involves structures like event queues, highlayer communication channels, and time-outs. To contain the complexity, we implement our verification tool with a newly developed BDD-like data-structure, reduced CRD (Clock-Restriction Diagram), which has enhanced the verification performance through intensive data-sharing in a previous report. However, the representation of reduced CRD does not allow for quick test of zone containment. To this purpose, we thus have designed a new CRD-based representation, cascade CRD, which has given us enough performance enhancement to successfully verifying several implementations of the web-camera.

Symbolic parametric safety analysis of linear hybrid systems with BDD-like data-structures

“…In the last several years, people have explored this approach in the hope of duplicating the success of BDD techniques [10], [12] in hardware verification for the verification of timed automata [2], [9], [11], [18], [21], [22], [23], [24], [25]. Our HRD can be seen as a variation of CDD (Clock-Difference Diagram) [11] and an extension of CRD (Clock-Restriction Diagram) [23], [24] for timed systems. The decision atoms in a CRD are all clock differences like x À x 0 .…”

“…We have implemented our ideas in our tool RED, version 5.3, which has been previously reported in [21], [22], [23], [24], [25] for the verification of timed automata. RED 5.3 supports full TCTL model-checking/simulation with graphical user-interface.…”

“…Others have developed separate representation schemes for the discrete part and continuous part of LHA [1], [3], [4], [7]. According to previous experiences [10], [12], [23], [24], [25], it can be more efficient to have a unified data-structure for both the discrete part and the continuous part. Moreover, the schemes used in [1], [3], [4], [7] only represent convex polyhedra in LHA state-space (concave polyhedra have to be represented as sets of convex ones) and suffer from the limitation to share common representation structures in different convex polyhedra.…”

Can Decision Diagrams Overcome State Space Explosion in Real-Time Verification?

“…The most common data structure for representing sets of configurations are Difference Bound Matrices (DBMs) [14]. More recently, Binary Decision Diagrams and Clock Difference Diagrams were applied to the verification of timed automata and were shown to be more efficient for many models [7,9,11,17,18]. In the following, these two data structures are introduced.…”

“…More recently, binary decision diagrams (BDDs) [12] and clock difference diagrams (CDDs) [7] (and their variants difference decision diagram [17] and clock restriction diagram [18]) were used to represent sets of configurations and were shown to be more efficient than DBMs for many models [7,9,11,17,18]. Although empirical performance results were published, important questions remained unanswered: (1) For which models are CDDs smaller than BDDs, and vice versa?…”