Verification in Continuous Time Recent Advances

Transcription

1 Verification in Continuous Time Recent Advances Hongyang Qu Department of Automatic Control and Systems Engineering University of Sheffield 10 March 2017

2 Outline Motivation Probabilistic models Real-time models Probabilistic real-time models Hybrid models Future work: Probabilistic hybrid models

3 Motivation Models with continuous time can be more accurate for verification of autonomous systems Sensors have time constraints Kinematic operations take time Control algorithms take time Adina Aniculaesei, Daniel Arnsberger, Falk Howar, Andreas Rausch: Towards the Verification of Safety-critical Autonomous Systems in Dynamic Environments. 2016: 79-90

4 Continuous time Markov Chains (CTMCs) Transitions can be triggered at any time instant Delay is modelled by exponential distributions

5 Verification techniques for CTMCs Value iteration Linear programming Simulation

6 PRISM The most popular probabilistic model checker Support DTMC/MDP/CTMC and other probabilistic models Support PCTL/CSL/LTL logics and reward structure Various verification engines

7 Continuous time Markov Decision Processes (CTMDPs) CTMC + MDP Verification techniques for CTMCs can applied to CTMDPs Need to solve scheduler selection Martin R. Neuhäußer, Lijun Zhang: Time-Bounded Reachability Probabilities in Continuous-Time Markov Decision Processes. QEST 2010:

8 Timed Automata (TAs) Modelling real-time clocks Clocks run at the same speed and can be reset Simple time constraints on clocks Peter Niebert, Hongyang Qu: Adding Invariants to Event Zone Automata. FORMATS 2006:

9 Verification techniques for TAs DBM (Difference Bound Matrices) RED (Region Encoding Diagram) CRD (Clock-Restriction Diagrams) BMC (Bounded Model Checking) BDD (Binary Decision Diagrams) Assume-Guarantee (compositional) reasoning

10 UPPAAL The most popular model checker for timed automata Sophisticated GUI Support TCTL logics Based on DBM

11 RED/REDLIB Symbolic model checker for timed automata Support TCTL logics Support CRD and HRD Farn Wang: Efficient verification of timed automata with BDD-like data structures. STTT 6(1): (2004)

12 PAT Automatic compositional verification of Event- Recording Automata Also support discrete models using partial order reduction and various techniques Shang-Wei Lin, Yang Liu, Jun Sun, Jin Song Dong, Étienne André: Automatic Compositional Verification of Timed Systems. FM 2012:

13 Timed Petri-Net Serge Haddad: Time and Timed Petri Nets.

14 Probabilistic Timed Automata (PTAs) MDP + Timed automata Mohammed Y. Hazim, Hongyang Qu, Sandor M. Veres: Testing, Verification and Improvements of Timeliness in ROS Processes. TAROS 2016:

15 Probabilistic Timed Programs Klaus Dräger, Marta Z. Kwiatkowska, David Parker, Hongyang Qu: Local abstraction refinement for probabilistic timed programs. Theor. Comput. Sci. 538: (2014)

16 Verification techniques for PTAs Digital clock Two-player stochastic games Local abstraction refinement

17 Timed Game Automata Controllable and uncontrollable actions Uncontrollable actions have higher priority Reachability control problem is to find a winning strategy such that all runs in the strategy satisfy a property Gerd Behrmann, Agnès Cougnard, Alexandre David, Emmanuel Fleury, Kim Guldstrand Larsen, Didier Lime: UPPAAL-Tiga: Time for Playing Games! CAV 2007:

18 UPPAAL-TIGA

19 Hybrid Automata Timed automata + continuous variables Linear hybrid automata can be solved by HRD Olaf Müller, Thomas Stauner: Modelling and Verification using Linear Hybrid Automata - a Case Study. Mathematical Modelling of Systems 1(1):

20 KeYmaera X Automated and interactive theorem prover for hybrid automata Support some non-linear fequations

21 Probabilistic hybrid models Generally undecidable Can be processed by approximation Marta Kwiatkowska, Ernst Moritz Hahn, Holger Hermanns, Arnd Hartmanns: Model Checking for Model Checking for Probabilistic Hybrid Systems. CPSWeek 2013