Counterexamples in Probabilistic Model Checking

This paper considers algorithms for counterexample generation for (bounded) probabilistic reachability properties in fully probabilistic systems. Finding the strongest evidence (i.e, the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that aremostly deviating from the required probability bound can be computed by adopting (partially new hopconstrained) k shortest paths algorithms that dynamically determine k.

[1]  K. Jacobs OSI-an appropriate basis for group communication? , 1989, IEEE International Conference on Communications, World Prosperity Through Communications,.

[2]  Matthias Nicola,et al.  Improving Performance in Replicated Databases through Relaxed Coherency , 1995, VLDB.

[3]  U. Naumann Syntax-Directed Derivative Code (Part I: Tangent-Linear Code) , 2005 .

[4]  Jürgen Giesl,et al.  Size-Change Termination for Term Rewriting , 2003, RTA.

[5]  Stefan Kahrs Polymorphic Type Checking by Interpretation of Code , 1992 .

[6]  Heiko Vogler,et al.  Compiler-based implementation of syntax-directed functional programming , 2009 .

[7]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[8]  Michael Hanus,et al.  Specialization of functional logic programs based on needed narrowing , 2004, Theory and Practice of Logic Programming.

[9]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[10]  Berthold Vöcking,et al.  Decision-making based on approximate and smoothed Pareto curves , 2007, Theor. Comput. Sci..

[11]  Nicos Christofides,et al.  An efficient implementation of an algorithm for finding K shortest simple paths , 1999, Networks.

[12]  Francisco Casacuberta,et al.  Probabilistic finite-state machines - part I , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Thomas Noll,et al.  Algebraic Correctness Proofs for Compiling Recursive Function Definitions with Strictness Information , 2006, Acta Informatica.

[14]  C. Lewerentz,et al.  Integrated Project Team Management in a Software Development Environment , 1988 .

[15]  T. Lindvall ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

[16]  Christel Baier,et al.  Comparative branching-time semantics for Markov chains , 2005, Inf. Comput..

[17]  Thomas Wilke,et al.  CTL+ is Exponentially more Succinct than CTL , 1999, FSTTCS.

[18]  Rutger F. H. Hofman,et al.  Parallelization of Branch-and-Bound Algorithms in a Functional Programming Environment , 1992 .

[19]  Manfred A. Jeusfeld,et al.  An Executable Meta Model for Re-Engineering of Database Schemas , 1994, Int. J. Cooperative Inf. Syst..

[20]  Jürgen Giesl,et al.  Transformation techniques for context-sensitive rewrite systems , 2004, J. Funct. Program..

[21]  Werner Hans,et al.  Full Indexing for Lazy Narrowing , 1993 .

[22]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[23]  Nicos Christofides,et al.  An efficient implementation of an algorithm for finding K shortest simple paths , 1999, Networks.

[24]  Janis A. Bubenko,et al.  Requirements Engineering: An Integrated View of Representation, Process, and Domain , 1993, ESEC.

[25]  Christof Löding,et al.  Solving the Sabotage Game Is PSPACE-Hard , 2003, MFCS.

[26]  Subhash Suri,et al.  Finding the k shortest simple paths , 2007, ALENEX.

[27]  Giuseppe Cattaneo,et al.  Algorithm engineering , 1999, CSUR.

[28]  Mayur Naik,et al.  From symptom to cause: localizing errors in counterexample traces , 2003, POPL '03.

[29]  Guido Moerkotte,et al.  Efficient Evaluation of Aggregates on Bulk Types , 1995, DBPL.

[30]  Matthias Jarke,et al.  Quality Information Systems: Repository Support for Evolving Process Models , 1992 .

[31]  Bernhard Steffen,et al.  An Elementary Bisimulation Decision Procedure for Arbitrary Context-Free Processes , 1995, MFCS.

[32]  Thomas A. Henzinger,et al.  Detecting Errors Before Reaching Them , 2000, CAV.

[33]  R. Studer,et al.  Survey on the Scenario Use in Twelve Selected Industrial Projects , 1998 .

[34]  Bernhard Steffen,et al.  Characteristic Formulae for Processes with Divergence , 1994, Inf. Comput..

[35]  Mesut Gunes,et al.  From Simulations to Testbeds — Architecture of the Hybrid MCG-Mesh Testbed , 2006 .

[36]  Manfred Nagl,et al.  A universal component for the administration in distributed and integrated development environments , 1994 .

[37]  Holger Hermanns,et al.  Discrete-time rewards model-checked (to appear) , 2003 .

[38]  Marta M. B. Pascoal,et al.  A new implementation of Yen’s ranking loopless paths algorithm , 2003, 4OR.

[39]  P. Rossmanith,et al.  A New Satisabilit y Algorithm With Applications To Max-Cut , 2005 .

[40]  Jürgen Giesl,et al.  Termination of term rewriting using dependency pairs , 2000, Theor. Comput. Sci..

[41]  Thomas Noll,et al.  Optimization of Straight-Line Code Revisited , 2006, Softwaretechnik-Trends.

[42]  Matthias Jarke,et al.  Intelligent Networks as a Data Intensive Application (INDIA) , 1994, ADB.

[43]  RWTHAachen,LehrstuhlfurInformatikII Ahornstrae55,W-5100Aachen,Germany , .

[44]  Marsha Chechik,et al.  Proof-Like Counter-Examples , 2003, TACAS.

[45]  Berthold Vöcking,et al.  Adaptive routing with stale information , 2005, PODC '05.

[46]  Henry N. Adorna 3-Party Message Complexity is Better than 2-Party Ones for Proving Lower Bounds on the Size of Minimal Nondeterministic Finite Automata , 2001, DCFS.

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

[48]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[49]  Manfred Nagl,et al.  On Integration Mechanisms within a Graph-based Software Development Environment , 1987, WG.

[50]  Stefan Gruner Einige Anmerkungen zur graphgrammatischen Spezifikation von Integrationswerkzeugen nach Westfechtel, Janning, Lefering und Schürr , 1998 .

[51]  George Horatiu Botorog High level parallel programming and the efficient implementation of numerical algorithms , 1998 .

[52]  Johannes Faassen,et al.  Using Full Parallel Boltzmann Machines for Optimization , 1997 .

[53]  Matthias Jarke,et al.  ConceptBase - A Deductive Object Base Manager , 1994 .

[54]  Bernhard Steffen,et al.  Compositional Minimization of Finite State Systems , 1990, CAV.

[55]  Andy Schürr,et al.  Graph Grammar Engineering with PROGRES , 1995, ESEC.

[56]  Jürgen Giesl,et al.  Innermost Termination of Context-Sensitive Rewriting , 2002, Developments in Language Theory.

[57]  Joost-Pieter Katoen,et al.  Discrete-Time Rewards Model-Checked , 2003, FORMATS.

[58]  Felix C. Freiling,et al.  An offensive approach to teaching information security : 'Aachen summer school applied IT security , 2005 .

[59]  Yuxiao Hu,et al.  Optimal vertex elimination in single-expression-use graphs , 2008, TOMS.

[60]  Orna Grumberg,et al.  A game-based framework for CTL counterexamples and 3-valued abstraction-refinement , 2007, TOCL.

[61]  Husain Aljazzar,et al.  Extended Directed Search for Probabilistic Timed Reachability , 2006, FORMATS.

[62]  Kurt Mehlhorn,et al.  Resource Constrained Shortest Paths , 2000, ESA.

[63]  M. J. Plasmeijer,et al.  Automatic Parallelization of Lazy Functional Programs , 1992 .

[64]  On Decidability of Unifiability modulo Rewrite Systems , 1996 .

[65]  Subhash Suri,et al.  Finding the k Shortest Simple Paths: A New Algorithm and Its Implementation. , 2003 .

[66]  Thomas Arts,et al.  Verifying Generic Erlang Client-Server Implementations , 2000, IFL.

[67]  Rance Cleaveland,et al.  The concurrency workbench: a semantics-based tool for the verification of concurrent systems , 1993, TOPL.

[68]  Kim G. Larsen,et al.  Optimal scheduling using priced timed automata , 2005, PERV.

[69]  Felix C. Freiling,et al.  Optimal Randomized Fair Exchange with Secret Shared Coins , 2005, OPODIS.

[70]  Andrew J. Viterbi,et al.  Error bounds for convolutional codes and an asymptotically optimum decoding algorithm , 1967, IEEE Trans. Inf. Theory.

[71]  Matthias Jarke,et al.  Exploring the Semantic Structure of Technical Document Collections: A Cooperative Systems Approach , 2000, CoopIS.

[72]  Matthias Jarke,et al.  Business process oriented information management: conceptual models at work , 1995, COCS '95.

[73]  Edmund M. Clarke,et al.  Counterexample-Guided Abstraction Refinement , 2000, CAV.

[74]  Benedikt Bollig,et al.  Local Parallel Model Checking for the Alternation-Free µ-Calculus , 2002, SPIN.

[75]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[76]  Matthias Nicola,et al.  Design and Evaluation of Wireless Health Care Information Systems in Developing Countries , 1998 .

[77]  Christian Prehofer,et al.  Higher-order narrowing with definitional trees , 1999, Journal of Functional Programming.

[78]  Dynamic Detect ion of Determinism in Functional Logic Languages , .

[79]  S. Gruner Fine-grained and Structure-Oriented Document Integration Tools are Needed for Development Processes , 2007 .

[80]  Helmut Veith,et al.  Tree-like counterexamples in model checking , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[81]  Kai Jakobs,et al.  Timer Handling in High-Performance Transport Systems , 1993, Integrated Broadband Communications.

[82]  OptimalPredictionLudwig Staiger A Tight Upper Bound on Kolmogorov Complexity by Hausdorr Dimension and Uniformly Optimal Prediction , 1995 .

[83]  Herbert Kuchen,et al.  Comparison of Dynamic Load Balancing Strategies , 1990 .

[84]  J. J. Ruzz,et al.  A VHDL Speci cation of a Shared Memory Parallel Machine for Babel , 1998 .

[85]  Thorsten Holz,et al.  A Pointillist Approach for Comparing Honeypots , 2005, DIMVA.

[86]  Felix C. Freiling,et al.  Revisiting Failure Detection and Consensus in Omission Failure Environments , 2005, ICTAC.

[87]  Uwe Naumann,et al.  Tangent-Linear Models by Augmented LL-Parsers , 2006, ICCSA.

[88]  Matthias Jarke,et al.  Model-driven planning and design of cooperative information systems , 1997 .

[89]  Bernhard Steffen,et al.  Generating Data Flow Analysis Algorithms from Modal Specifications , 1993, Sci. Comput. Program..

[90]  Felix C. Freiling,et al.  Botnet Tracking: Exploring a Root-Cause Methodology to Prevent Distributed Denial-of-Service Attacks , 2005, ESORICS.

[91]  Thorsten Holz,et al.  An Offensive Approach to Teaching Information Security , 2005 .

[92]  Wellington Santos Martins,et al.  Parallel Implementations of Functional Languages , 1992 .

[93]  Mike S. Paterson Algorithms - ESA 2000 , 2003, Lecture Notes in Computer Science.

[94]  Felix C. Freiling,et al.  Efficient Reductions for Wait-Free Termination Detection in Faulty Distributed Systems , 2005 .

[95]  Benedikt Bollig,et al.  Message-passing automata are expressively equivalent to EMSO logic , 2006, Theor. Comput. Sci..

[96]  Matthias Jarke,et al.  Three Aspects of Intelligent Cooperation in the Quality Cycle , 1993, Int. J. Cooperative Inf. Syst..

[97]  Markus Mohnen,et al.  Optimising the memory management of higher order functional programs , 1997 .

[98]  Guido Moerkotte,et al.  Nested Queries in Object Bases , 1993, DBPL.

[99]  Matthias Jarke,et al.  Towards a logic-based reconstruction of software configuration management , 1992, Proceedings of the Seventh Knowledge-Based Software Engineering Conference.

[100]  Rudolf Mathar,et al.  Analyzing routing strategy NFP in multihop packet radio networks on a line , 1995, IEEE Trans. Commun..

[101]  Andreas J. Winter,et al.  Modules and Updatable Graph Views for PROgrammed Graph REwriting Systems , 1997 .

[102]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[103]  U. Quernheim Satellite communication protocols-a performance comparison considering on-board processing , 1988, 8th European Conference on Electrotechnics, Conference Proceedings on Area Communication.

[104]  Matthias Jarke,et al.  From Relational to Object-Oriented Integrity Simplification , 1991, DOOD.

[105]  Jürgen Giesl,et al.  Deciding Inductive Validity of Equations , 2003, CADE.

[106]  Otto Spaniol,et al.  File transfer in high-speed token ring networks: performance evaluation by approximate analysis and simulation , 1988, IEEE J. Sel. Areas Commun..

[107]  Holger Hermanns,et al.  Counterexamples for Timed Probabilistic Reachability , 2005, FORMATS.

[108]  Markus Mohnen Efficient Compile-Time Garbage Collection for Arbitrary Data Structures , 1995, PLILP.

[109]  Martin Grohe,et al.  An existential locality theorem , 2004, Ann. Pure Appl. Log..

[110]  Andrés Marzal,et al.  Computing the K Shortest Paths: A New Algorithm and an Experimental Comparison , 1999, WAE.

[111]  David Eppstein,et al.  Finding the k Shortest Paths , 1999, SIAM J. Comput..

[112]  Thierry Cachat The Power of One-Letter Rational Languages , 2001, Developments in Language Theory.

[113]  Roland Baumann Client / Server Distribution in a Structure-Oriented Database Management System , 1997 .

[114]  Jürgen Giesl,et al.  Proving and Disproving Termination of Higher-Order Functions , 2005, FroCoS.

[115]  Andy Schürr,et al.  Nondeterministic Control Structures for Graph Rewriting Systems , 1991, WG.

[116]  Rudolf Mathar,et al.  On the distribution of cumulated interference power in Rayleigh fading channels , 1995, Wirel. Networks.

[117]  Stefan Gruner Schemakorrespondenzaxiome unterstützen die paargrammatische Spezifikation inkrementeller Integrationswerkzeuge , 1997 .

[118]  David E. Culler,et al.  Cl91] 5.1 Related Work 5.2 Further Work 4.4 Split Code 4.3 Implementing J*code 4.2.3 Some Examples 4.2 Extending Jcode 4.2.2 Creating Processes Equational Constraints, Residuation, and the Parallel Jump-machine , 1992 .

[119]  J. Klop,et al.  WST ’ 04 7 th International Workshop on Termination , 2004 .

[120]  Andy Schürr,et al.  Computing with Graphs and Graph Rewriting , 1999 .

[121]  Stackbased ReductionGuido Hogen,et al.  Parallel Functional Implementations: Graphbased vs. Stackbased Reduction , 1995 .

[122]  M. O. Berger,et al.  k-coloring vertices using a neural network with convergence to valid solutions , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[123]  Gottfried Vossen,et al.  SUXESS: Towards a Sound Unification of Extensions of the Relational Data Model , 1991, Data Knowl. Eng..

[124]  Marcin Jurdzinski,et al.  A Discrete Strategy Improvement Algorithm for Solving Parity Games , 2000, CAV.

[125]  David A. Rushall An Attribute Grammar Evaluator in Haskell , 1992 .

[126]  Rudolf Mathar,et al.  Analyzing a distributed slot assignment protocol by Markov chains , 1992, [1992 Proceedings] Vehicular Technology Society 42nd VTS Conference - Frontiers of Technology.

[127]  Matthias Jarke,et al.  Incremental Maintenance of Externally Materialized Views , 1996, VLDB.

[128]  Olivier Danvy,et al.  On the Idempotence of the CPS Transformation , 1996 .

[129]  John Glauert Parallel Implementation of Functional Languages Using Small Processes , 1996 .

[130]  Sven Helmer,et al.  An Experimental Study on the Complexity of Left-deep Join Ordering Problems for Cyclic Queries Fakultt at F Ur Informatik , 1995 .

[131]  Werner Hans,et al.  A Complete Indexing Scheme for WAM-based Abstract Machines , 1992, PLILP.

[132]  Benedikt Bollig,et al.  Deciding LTL over Mazurkiewicz traces , 2001, Proceedings Eighth International Symposium on Temporal Representation and Reasoning. TIME 2001.

[133]  Jirí Srba,et al.  Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets , 2008, FORMATS.

[134]  Patrick Shicheng Chen,et al.  On Inference Rules of Logic-Based Information Retrieval Systems , 1994, Inf. Process. Manag..

[135]  Berthold Vöcking,et al.  A Counterexample to the Fully Mixed Nash Equilibrium Conjecture , 2005 .

[136]  U. Naumann,et al.  Intraprocedural Adjoint Code Generated by the Differentiation-Enabled NAGWare Fortran Compiler , 2006 .

[137]  GrumbergOrna,et al.  A game-based framework for CTL counterexamples and 3-valued abstraction-refinement , 2007 .

[138]  Kavita Ravi,et al.  Fate and free will in error traces , 2004, International Journal on Software Tools for Technology Transfer.

[139]  Marta M. B. Pascoal,et al.  Deviation Algorithms for Ranking Shortest Paths , 1999, Int. J. Found. Comput. Sci..

[140]  Wolfgang Thomas,et al.  AMORE: A System for Computing Automata, MOnoids, and Regular Expressions , 1989, STACS.

[141]  Stefan Richter,et al.  A Faster Algorithm for the Steiner Tree Problem , 2006, STACS.

[142]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[143]  Werner Damm,et al.  Specifying distributed computer architectures in AADL , 1989, Parallel Comput..

[144]  Matthias Jarke,et al.  Simulating the Impact of Information Flows in Networked Organizations , 1996, ICIS.

[145]  Werner Hans,et al.  On the Interaction of Lazy Evaluation and Backtracking , 1992, PLILP.

[146]  Pieter H. Hartel,et al.  Statistics on storage management in a lazy functional language implementation , 1991 .