Discrete and continuous strategies for timed-arc Petri net games

Automatic strategy synthesis for a given control objective can be used to generate correct-by-construction controllers of real-time reactive systems. The existing symbolic approach for continuous timed game is a computationally hard task and current tools like UPPAAL TiGa often scale poorly with the model complexity. We suggest an explicit approach for strategy synthesis in the discrete-time setting and show that even for systems with closed guards, the existence of a safety discrete-time strategy does not imply the existence of a safety continuous-time strategy and vice versa. Nevertheless, we prove that the answers to the existence of discrete-time and continuous-time safety strategies coincide on a practically motivated subclass of urgent controllers that either react immediately after receiving an environmental input or wait with the decision until a next event is triggered by the environment. We then develop an on-the-fly synthesis algorithm for discrete timed-arc Petri net games. The algorithm is implemented in our tool TAPAAL, and based on the experimental evidence, we discuss the advantages of our approach compared to the symbolic continuous-time techniques.

[1]  Alan J. Hoffman,et al.  Integral Boundary Points of Convex Polyhedra , 2010, 50 Years of Integer Programming.

[2]  J. Raskin,et al.  Petri Games are Monotonic but Dicult to Decide , 2003 .

[3]  Stavros Tripakis,et al.  KRONOS: A Model-Checking Tool for Real-Time Systems (Tool-Presentation for FTRTFT '98) , 1998, FTRTFT.

[4]  Joseph Sifakis,et al.  Controller Synthesis for Timed Automata 1 , 1998 .

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

[6]  Rüdiger Ehlers,et al.  Synthia: Verification and Synthesis for Timed Automata , 2011, CAV.

[7]  Kim G. Larsen,et al.  UPPAAL-Tiga: Time for Playing Games! , 2007, CAV.

[8]  Leonid Ryzhyk,et al.  The Second Reactive Synthesis Competition (SYNTCOMP 2015) , 2016, SYNT.

[9]  A. Pnueli,et al.  CONTROLLER SYNTHESIS FOR TIMED AUTOMATA , 2006 .

[10]  Wang Yi,et al.  UPPAAL 4.0 , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[11]  Kim G. Larsen,et al.  Efficient On-the-Fly Algorithms for the Analysis of Timed Games , 2005, CONCUR.

[12]  Oded Maler,et al.  As Soon as Probable: Optimal Scheduling under Stochastic Uncertainty , 2013, TACAS.

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

[14]  Bernd Finkbeiner,et al.  Template-Based Controller Synthesis for Timed Systems , 2012, TACAS.

[15]  Kim G. Larsen,et al.  Memory Efficient Data Structures for Explicit Verification of Timed Systems , 2014, NASA Formal Methods.

[16]  Qiong Zhou,et al.  Generation of optimal control policy for flexible manufacturing cells: A Petri net approach , 1995 .

[17]  W. Marsden.  I and J , 2012 .

[18]  Robert Mattmüller,et al.  Component-Based Abstraction Refinement for Timed Controller Synthesis , 2009, 2009 30th IEEE Real-Time Systems Symposium.

[19]  Bernd Finkbeiner,et al.  Bounded Synthesis for Petri Games , 2015, Correct System Design.

[20]  Jason Cong,et al.  Scheduling with soft constraints , 2009, 2009 IEEE/ACM International Conference on Computer-Aided Design - Digest of Technical Papers.

[21]  Stavros Tripakis,et al.  Efficient Verification of Timed Automata Using Dense and Discrete Time Semantics , 1999, CHARME.

[22]  David de Frutos-Escrig,et al.  On non-decidability of reachability for timed-arc Petri nets , 1999, PNPM.

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

[24]  Kim G. Larsen,et al.  PTrie: Data Structure for Compressing and Storing Sets via Prefix Sharing , 2017, ICTAC.

[25]  Scott A. Smolka,et al.  Simple Linear-Time Algorithms for Minimal Fixed Points (Extended Abstract) , 1998, ICALP.

[26]  Kim G. Larsen,et al.  On Zone-Based Analysis of Duration Probabilistic Automata , 2010, INFINITY.

[27]  Jirí Srba,et al.  Verification of Liveness Properties on Closed Timed-Arc Petri Nets , 2012, MEMICS.

[28]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[29]  Bernd Finkbeiner,et al.  Petri games: Synthesis of distributed systems with causal memory , 2014, Inf. Comput..

[30]  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.

[31]  Jirí Srba,et al.  Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets , 2014, FORMATS.

[32]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[33]  Jirí Srba,et al.  Soundness of Timed-Arc Workflow Nets in Discrete and Continuous-Time Semantics , 2015, Fundam. Informaticae.

[34]  Didier Lime,et al.  Romeo: A Tool for Analyzing Time Petri Nets , 2005, CAV.

[35]  François Vernadat,et al.  Time Petri Nets Analysis with TINA , 2006, Third International Conference on the Quantitative Evaluation of Systems - (QEST'06).

[36]  Kim G. Larsen,et al.  Time-Darts: A Data Structure for Verification of Closed Timed Automata , 2012, SSV.

[37]  Alonzo Church,et al.  Logic, arithmetic, and automata , 1962 .

[38]  Wang Yi,et al.  Time-abstracted Bisimulation: Implicit Specifications and Decidability , 1997, Inf. Comput..

[39]  David L. Dill,et al.  Timing Assumptions and Verification of Finite-State Concurrent Systems , 1989, Automatic Verification Methods for Finite State Systems.