Stubborn Set Reduction for Timed Reachability and Safety Games

Timed games are an essential formalism for modeling timesensitive reactive systems that must respond to uncontrollable events triggered by the (hostile) environment. However, the control synthesis problem for these systems is often resource-demanding due to the state space explosion problem. To counter this problem, we present an extension of partial order reduction, based on stubborn sets, into timed games. We introduce the theoretical foundations on the general formalism of timed game labeled transition systems and then instantiate it to the model of timed-arc Petri net games. We provide an efficient implementation of our method as part of the model checker TAPAAL and discuss an experimental evaluation on several case studies that show increasing (sometimes even exponential) savings in time and memory as the case studies scale to larger instances. To the best of our knowledge, this is the first application of partial order reductions to a game formalism that includes time.

[1]  W. Marsden.  I and J , 2012 .

[2]  George S. Avrunin,et al.  A benchmark for evaluating software engineering techniques for improving medical processes , 2010, SEHC '10.

[3]  Kim G. Larsen,et al.  Real-Time Strategy Synthesis for Timed-Arc Petri Net Games via Discretization , 2016, SPIN.

[4]  Kamel Barkaoui,et al.  Delay-dependent partial order reduction technique for real time systems , 2017, Real-Time Systems.

[5]  Kim Guldstrand Larsen,et al.  Stubborn Set Reduction for Two-Player Reachability Games , 2019, Log. Methods Comput. Sci..

[6]  Thomas A. Henzinger,et al.  Parametric real-time reasoning , 1993, STOC.

[7]  Marco Muñiz,et al.  The Wireless Fire Alarm System: Ensuring Conformance to Industrial Standards through Formal Verification , 2014, FM.

[8]  Gorjan Alagic,et al.  #p , 2019, Quantum information & computation.

[9]  Peter Niebert,et al.  Partial Order Reductions for Bisimulation Checking , 1998, FSTTCS.

[10]  Somesh Jha,et al.  Exploiting symmetry in temporal logic model checking , 1993, Formal Methods Syst. Des..

[11]  Jirí Srba,et al.  TAPAAL 2.0: Integrated Development Environment for Timed-Arc Petri Nets , 2012, TACAS.

[12]  Robert H. Sloan,et al.  Stubborn Sets for Real-Time Petri Nets , 1997, Formal Methods Syst. Des..

[13]  Antti Valmari,et al.  Stubborn set methods for process algebras , 1997, Partial Order Methods in Verification.

[14]  Kim G. Larsen,et al.  Partial Order Reduction for Reachability Games , 2019, CONCUR.

[15]  Kim G. Larsen,et al.  Start Pruning When Time Gets Urgent: Partial Order Reduction for Timed Systems , 2018, CAV.

[16]  Antti Valmari,et al.  Stubborn sets for reduced state space generation , 1991, Applications and Theory of Petri Nets.

[17]  Parosh Aziz Abdulla,et al.  General decidability theorems for infinite-state systems , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[18]  Doron A. Peled,et al.  All from One, One for All: on Model Checking Using Representatives , 1993, CAV.

[19]  Antti Valmari,et al.  A stubborn attack on state explosion , 1990, Formal Methods Syst. Des..

[20]  Tommaso Bolognesi,et al.  From timed Petri nets to timed LOTOS , 1990, PSTV.

[21]  Tomohiro Yoneda,et al.  Efficient Verification of Parallel Real–Time Systems , 1993, Formal Methods Syst. Des..

[22]  Antti Valmari,et al.  Stubborn Set Intuition Explained , 2016, PNSE @ Petri Nets.

[23]  Michael R. Hansen,et al.  Synthesis of Railway-Signaling Plans using Reachability Games , 2016, IFL 2016.

[24]  Wang Yi,et al.  Partial Order Reductions for Timed Systems , 1998, CONCUR.

[25]  Antti Valmari.  A stubborn attack on state explosion , 1992, Formal Methods Syst. Des..

[26]  Wojciech Penczek,et al.  A partial order approach to branching time logic model checking , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[27]  Pierre Wolper,et al.  Using partial orders for the efficient verification of deadlock freedom and safety properties , 1991, Formal Methods Syst. Des..

[28]  Thomas Neele,et al.  Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems , 2019, TACAS.

[29]  Jirí Srba,et al.  TAPAAL and Reachability Analysis of P/T Nets , 2016, Trans. Petri Nets Other Model. Concurr..

[30]  Kamel Barkaoui,et al.  Stubborn Sets for Time Petri Nets , 2015, ACM Trans. Embed. Comput. Syst..

[31]  Johan Lilius,et al.  Efficient State Space Search for Time Petri Nets , 1998, MFCS Workshop on Concurrency.

[32]  Marius Minea,et al.  Partial Order Reduction for Model Checking of Timed Automata , 1999, CONCUR.

[33]  Kamel Barkaoui,et al.  Reducing Interleaving Semantics Redundancy in Reachability Analysis of Time Petri Nets , 2013, TECS.

[34]  Hans-Michael Hanisch.  Analysis of Place/Transition Nets with Timed Arcs and its Application to Batch Process Control , 1993, Application and Theory of Petri Nets.

[35]  Somesh Jha,et al.  Combining Partial Order and Symmetry Reductions , 1997, TACAS.

[36]  Somesh Jha,et al.  Exploiting Symmetry In Temporal Logic Model Checking , 1993, CAV.

[37]  Andreas Podelski,et al.  Ready for testing: ensuring conformance to industrial standards through formal verification , 2016, Formal Aspects of Computing.

[38]  Pierre Wolper,et al.  Using partial orders for the efficient verification of deadlock freedom and safety properties , 1991, Formal Methods Syst. Des..

[39]  A. Prasad Sistla,et al.  Reasoning about systems with many processes , 1992, JACM.

[40]  Doron A. Peled,et al.  Combining partial order reductions with on-the-fly model-checking , 1994, Formal Methods Syst. Des..

[41]  Patrice Godefroid,et al.  Partial-Order Methods for the Verification of Concurrent Systems , 1996, Lecture Notes in Computer Science.

[42]  Kim G. Larsen,et al.  Discrete and continuous strategies for timed-arc Petri net games , 2017, International Journal on Software Tools for Technology Transfer.