Computing branching distances with quantitative games

We lay out a general method for computing branching distances between labeled transition systems. We translate the quantitative games used for defining these distances to other, path-building games which are amenable to methods from the theory of quantitative games. We then show for all common types of branching distances how the resulting path-building games can be solved. In the end, we achieve a method which can be used to compute all branching distances in the linear-time–branching-time spectrum.

[1]  Farn Wang,et al.  Symbolic Model Checking for Distributed Real-Time Systems , 1993, FME.

[2]  Kim G. Larsen,et al.  Metrics for weighted transition systems: Axiomatization and complexity , 2011, Theor. Comput. Sci..

[3]  Jirí Srba,et al.  TAPAAL: Editor, Simulator and Verifier of Timed-Arc Petri Nets , 2009, ATVA.

[4]  P. Merlin,et al.  Recoverability of Communication Protocols - Implications of a Theoretical Study , 1976, IEEE Transactions on Communications.

[5]  Stéphane Gaubert,et al.  How to solve large scale deterministic games with mean payoff by policy iteration , 2006, valuetools '06.

[6]  Kim G. Larsen,et al.  A Quantitative Characterization of Weighted Kripke Structures in Temporal Logic , 2009, MEMICS.

[7]  Kim G. Larsen,et al.  Weighted modal transition systems , 2012, Formal Methods Syst. Des..

[8]  Benjamin Monmege,et al.  Pseudopolynomial iterative algorithm to solve total-payoff games and min-cost reachability games , 2017, Acta Informatica.

[9]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[10]  Jan Friso Groote,et al.  Structured Operational Semantics and Bisimulation as a Congruence , 1992, Inf. Comput..

[11]  Kim G. Larsen,et al.  Quantitative analysis of weighted transition systems , 2010, J. Log. Algebraic Methods Program..

[12]  James Worrell,et al.  The Complexity of Computing a Bisimilarity Pseudometric on Probabilistic Automata , 2014, Horizons of the Mind.

[13]  François Laviolette,et al.  Approximate Analysis of Probabilistic Processes: Logic, Simulation and Games , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[14]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

[15]  Thomas A. Henzinger,et al.  Discounting the Future in Systems Theory , 2003, ICALP.

[16]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[17]  Radha Jagadeesan,et al.  Metrics for labelled Markov processes , 2004, Theor. Comput. Sci..

[18]  Axel Legay,et al.  Computing Branching Distances Using Quantitative Games , 2019, ICTAC.

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

[20]  Thomas A. Henzinger,et al.  HYTECH: a model checker for hybrid systems , 1997, International Journal on Software Tools for Technology Transfer.

[21]  Stephen Gilmore,et al.  The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling , 1994, Computer Performance Evaluation.

[22]  Nancy A. Lynch,et al.  Probabilistic Simulations for Probabilistic Processes , 1994, Nord. J. Comput..

[23]  Axel Legay,et al.  The quantitative linear-time-branching-time spectrum , 2011, Theor. Comput. Sci..

[24]  Thomas A. Henzinger,et al.  Quantifying Similarities Between Timed Systems , 2005, FORMATS.

[25]  A. Ehrenfeucht An application of games to the completeness problem for formalized theories , 1961 .

[26]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[27]  Martin Fränzle,et al.  HySAT: An efficient proof engine for bounded model checking of hybrid systems , 2007, Formal Methods Syst. Des..

[28]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum I , 2001, Handbook of Process Algebra.

[29]  Axel Legay,et al.  The quantitative linear-time-branching-time spectrum , 2014, Theor. Comput. Sci..

[30]  Axel Legay,et al.  General Quantitative Specification Theories with Modalities , 2012, CSR.

[31]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[32]  Luca de Alfaro,et al.  Linear and Branching System Metrics , 2009, IEEE Transactions on Software Engineering.

[33]  R. V. Glabbeek CHAPTER 1 – The Linear Time - Branching Time Spectrum I.* The Semantics of Concrete, Sequential Processes , 2001 .

[34]  Marta Z. Kwiatkowska,et al.  Probabilistic symbolic model checking with PRISM: a hybrid approach , 2004, International Journal on Software Tools for Technology Transfer.

[35]  Ron Koymans,et al.  Specifying real-time properties with metric temporal logic , 1990, Real-Time Systems.

[36]  Orna Kupferman,et al.  Making Weighted Containment Feasible: A Heuristic Based on Simulation and Abstraction , 2012, CONCUR.

[37]  Krishnendu Chatterjee,et al.  Quantitative fair simulation games , 2017, Inf. Comput..

[38]  Kim G. Larsen,et al.  Quantitative Refinement for Weighted Modal Transition Systems , 2011, MFCS.

[39]  Dejan Nickovic,et al.  Robustness of Sequential Circuits , 2010, 2010 10th International Conference on Application of Concurrency to System Design.

[40]  Kim G. Larsen,et al.  Infinite Runs in Weighted Timed Automata with Energy Constraints , 2008, FORMATS.

[41]  Axel Legay,et al.  A linear-time-branching-time spectrum for behavioral specification theories , 2020, J. Log. Algebraic Methods Program..

[42]  Antoine Girard,et al.  Approximation Metrics for Discrete and Continuous Systems , 2006, IEEE Transactions on Automatic Control.

[43]  Bengt Jonsson,et al.  A logic for reasoning about time and reliability , 1990, Formal Aspects of Computing.

[44]  James Worrell,et al.  A behavioural pseudometric for probabilistic transition systems , 2005, Theor. Comput. Sci..

[45]  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.

[46]  Uri Zwick,et al.  The Complexity of Mean Payoff Games on Graphs , 1996, Theor. Comput. Sci..

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

[48]  Robert K. Brayton,et al.  Model-checking continuous-time Markov chains , 2000, TOCL.

[49]  Thomas A. Henzinger,et al.  Model checking discounted temporal properties , 2005, Theor. Comput. Sci..

[50]  Axel Legay,et al.  A Linear-Time-Branching-Time Spectrum of Behavioral Specification Theories , 2016, SOFSEM.

[51]  Axel Legay,et al.  General quantitative specification theories with modal transition systems , 2014, Acta Informatica.

[52]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[53]  Kim G. Larsen,et al.  Bisimulation through probabilistic testing (preliminary report) , 1989, POPL '89.

[54]  Axel Legay,et al.  A Robust Specification Theory for Modal Event-Clock Automata , 2012, FIT.

[55]  Wang Yi,et al.  Uppaal in a nutshell , 1997, International Journal on Software Tools for Technology Transfer.

[56]  Franck van Breugell An introduction to metric semantics: operational and denotational models for programming and specification languages , 2001 .

[57]  Thomas A. Henzinger,et al.  Symbolic Model Checking for Real-Time Systems , 1994, Inf. Comput..

[58]  Colin Stirling,et al.  Modal and Temporal Logics for Processes , 1996, Banff Higher Order Workshop.

[59]  Axel Legay,et al.  Compositionality for quantitative specifications , 2014, FACS.

[60]  Krishnendu Chatterjee,et al.  Quantitative languages , 2008, TOCL.

[61]  Thomas A. Henzinger,et al.  From Model Checking to Model Measuring , 2013, CONCUR.

[62]  A. Ehrenfeucht,et al.  Positional strategies for mean payoff games , 1979 .

[63]  J. Neumann Zur Theorie der Gesellschaftsspiele , 1928 .