An Abstraction Framework for Mixed Non-deterministic and Probabilistic Systems

We study abstraction techniques for model checking systems that combine non-deterministic with probabilistic behavior, emphasizing the discrete case. Existing work on abstraction offers a host of isolated techniques which we discuss uniformly through the formulation of abstracted model-checking problems (MCPs). Although this conceptualization is primarily meant to be a useful focal point for surveying the literature on abstraction-based model checking even beyond such combined systems, it also opens up new research opportunities and challenges for abstract model checking of mixed systems. In particular, we sketch how quantitative domain theory may be used to specify the precision of answers obtained from abstract model checks.

[1]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[2]  Scott A. Smolka,et al.  CCS expressions, finite state processes, and three problems of equivalence , 1983, PODC '83.

[3]  Stephen Gilmore,et al.  Language constructs for describing features : proceedings of the FIREworks workshop , 2001 .

[4]  Michael Huth,et al.  Quantitative analysis and model checking , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[5]  R. I. Bahar,et al.  Algebraic decision diagrams and their applications , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[6]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[7]  Annabelle McIver,et al.  Almost-Certain Eventualities and Abstract Probabilities in the Temporal Logic PTL , 2001, CATS.

[8]  Klaus Keimel,et al.  Domains and Processes , 2001 .

[9]  Pierre-Yves Schobbens,et al.  Approximating ATL* in ATL , 2002, VMCAI.

[10]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[11]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[12]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[13]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[14]  Michael Huth.  The Interval Domain: A Matchmaker for aCTL and aPCTL , 1998, Electron. Notes Theor. Comput. Sci..

[15]  Kim G. Larsen,et al.  Modal Specifications , 1989, Automatic Verification Methods for Finite State Systems.

[16]  Rajeev Motwani,et al.  Randomized algorithms , 1996, CSUR.

[17]  Marta Z. Kwiatkowska,et al.  Probabilistic Model Checking of the IEEE 802.11 Wireless Local Area Network Protocol , 2002, PAPM-PROBMIV.

[18]  Armin Biere,et al.  Bounded Model Checking Using Satisfiability Solving , 2001, Formal Methods Syst. Des..

[19]  Roberto Segala,et al.  Decision Algorithms for Probabilistic Bisimulation , 2002, CONCUR.

[20]  R. Milner,et al.  Bigraphical Reactive Systems , 2001, CONCUR.

[21]  David Monniaux.  An abstract Monte-Carlo method for the analysis of probabilistic programs , 2001, POPL '01.

[22]  Michael Huth,et al.  A Unifying Framework for Model Checking Labeled Kripke Structures, Modal Transition Systems and Interval Transition Systems , 1999, FSTTCS.

[23]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[24]  C. Jones,et al.  A probabilistic powerdomain of evaluations , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[25]  David Monniaux,et al.  Analyse de programmes probabilistes par interprétation abstraite , 2001 .

[26]  Dorothy E. Denning,et al.  A lattice model of secure information flow , 1976, CACM.

[27]  Dexter Kozen.  A Probabilistic PDL , 1985, J. Comput. Syst. Sci..

[28]  Hans A. Hansson.  Time and probability in formal design of distributed systems , 1991, DoCS.

[29]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[30]  Pawel Waszkiewicz,et al.  Quantitative Continuous Domains , 2003, Appl. Categorical Struct..

[31]  Mihalis Yannakakis,et al.  The complexity of probabilistic verification , 1995, JACM.

[32]  Holger Hermanns,et al.  Interactive Markov Chains , 2002, Lecture Notes in Computer Science.

[33]  Emden R. Gansner,et al.  A C++ data model supporting reachability analysis and dead code detection , 1997, ESEC '97/FSE-5.

[34]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

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

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

[37]  James C. Corbett,et al.  A Formal Study of Slicing for Multi-threaded Programs with JVM Concurrency Primitives , 1999, SAS.

[38]  Joseph Sifakis,et al.  Automatic Verification Methods for Finite State Systems , 1989, Lecture Notes in Computer Science.

[39]  James Hirschorn,et al.  Measure Theory, I , 2003 .

[40]  Patrick Cousot,et al.  Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints , 1977, POPL.

[41]  Keye Martin,et al.  The Measurement Process in Domain Theory , 2000, ICALP.

[42]  K. Larsen,et al.  Reachability Analysis of Probabilistic Systems by Successive Refinements , 2001, PAPM-PROBMIV.

[43]  Patrice Godefroid,et al.  Model Checking Partial State Spaces with 3-Valued Temporal Logics , 1999, CAV.

[44]  Joost-Pieter Katoen,et al.  Process algebra for performance evaluation , 2002, Theor. Comput. Sci..

[45]  Chris Hankin,et al.  Approximate non-interference , 2002, Proceedings 15th IEEE Computer Security Foundations Workshop. CSFW-15.

[46]  Kim G. Larsen,et al.  A modal process logic , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[47]  Edmund M. Clarke,et al.  Model checking and abstraction , 1994, TOPL.

[48]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[49]  Michael Huth,et al.  Domains of View: A Foundation for Specification and Analysis , 2001 .

[50]  Insup Lee,et al.  Weak Bisimulation for Probabilistic Systems , 2000, CONCUR.

[51]  Dennis M. Volpano,et al.  Provably secure programming languages for remote evaluation , 1996, CSUR.

[52]  Joseph Sifakis,et al.  Readiness Semantics for Regular Processes with Silent Actions , 1987, ICALP.

[53]  Kousha Etessami,et al.  A Hierarchy of Polynomial-Time Computable Simulations for Automata , 2002, CONCUR.

[54]  Christel Baier,et al.  Deciding Bisimilarity and Similarity for Probabilistic Processes , 2000, J. Comput. Syst. Sci..

[55]  Annabelle McIver,et al.  Games, Probability and the Quantitative µ-Calculus qMµ , 2002, LPAR.

[56]  Ionel Bucur,et al.  Toposes, Algebraic Geometry and Logic , 1972 .

[57]  Kim G. Larsen,et al.  Reduction and Refinement Strategies for Probabilistic Analysis , 2002, PAPM-PROBMIV.

[58]  Rance Cleaveland,et al.  Testing Preorders for Probabilistic Processes , 1992, ICALP.

[59]  Michael Huth,et al.  Possibilistic and Probabilistic Abstraction-Based Model Checking , 2002, PAPM-PROBMIV.

[60]  Kenneth L. McMillan,et al.  Symbolic model checking , 1992 .

[61]  Radha Jagadeesan,et al.  Approximating labeled Markov processes , 2000, Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332).

[62]  Julian Bradfield.  Verifying Temporal Properties of Systems , 1992, Progress in Theoretical Computer Science.

[63]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[64]  Kousha Etessami,et al.  Optimizing Büchi Automata , 2000, CONCUR.

[65]  Patrice Godefroid,et al.  Generalized Model Checking: Reasoning about Partial State Spaces , 2000, CONCUR.

[66]  Stephen Gilmore,et al.  Language Constructs for Describing Features , 2001, Springer London.

[67]  K. Hofmann,et al.  A Compendium of Continuous Lattices , 1980 .

[68]  Joost-Pieter Katoen,et al.  Performance Evaluation : = (Process Algebra + Model Checking) × Markov Chains , 2001, CONCUR.

[69]  Samson Abramsky,et al.  Domain theory , 1995, LICS 1995.

[70]  Flemming Nielson,et al.  Principles of Program Analysis , 1999, Springer Berlin Heidelberg.

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

[72]  Christel Baier,et al.  Norm Functions for Probabilistic Bisimulations with Delays , 2000, FoSSaCS.

[73]  J. Baeten.  Applications of process algebra , 1990 .

[74]  J. Cheney,et al.  A sequent calculus for nominal logic , 2004, LICS 2004.

[75]  David Monniaux,et al.  Backwards Abstract Interpretation of Probabilistic Programs , 2001, ESOP.

[76]  David Monniaux.  Abstract interpretation of programs as Markov decision processes , 2005, Sci. Comput. Program..

[77]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

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

[79]  Annabelle McIver,et al.  Probabilistic predicate transformers , 1996, TOPL.

[80]  Kim G. Larsen,et al.  Timed Modal Specification - Theory and Tools , 1993, CAV.

[81]  Bran Selic.  Physical Programming: Beyond Mere Logic , 2001, FASE.

[82]  Kousha Etessami,et al.  Analysis of Recursive Game Graphs Using Data Flow Equations , 2004, VMCAI.

[83]  Abbas Edalat,et al.  Bisimulation for Labelled Markov Processes , 2002, Inf. Comput..

[84]  Annabelle McIver,et al.  Refinement-oriented probability for CSP , 1996, Formal Aspects of Computing.

[85]  Patrick Cousot,et al.  Temporal abstract interpretation , 2000, POPL '00.

[86]  Annabelle McIver,et al.  An Expectation-Transformer Model for Probabilistic Temporal Logic , 1999, Log. J. IGPL.

[87]  Peter J. Denning,et al.  Certification of programs for secure information flow , 1977, CACM.

[88]  Christos H. Papadimitriou,et al.  Games against nature , 1985, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[89]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[90]  Richard Lassaigne,et al.  Approximate Verification of Probabilistic Systems , 2002, PAPM-PROBMIV.

[91]  Lu Tian,et al.  On some equivalence relations for probabilistic processes , 1992, Fundamenta Informaticae.

[92]  Dexter Kozen,et al.  Semantics of probabilistic programs , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[93]  Christel Baier,et al.  Computing Probability Bounds for Linear Time Formulas over Concurrent Probabilistic Systems , 1998, PROBMIV.

[94]  Dennis Dams,et al.  Abstract interpretation and partition refinement for model checking , 1996 .

[95]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[96]  Herbert Wiklicky,et al.  Probabilistic Abstract Interpretation and Statistical Testing , 2002, PAPM-PROBMIV.

[97]  David Monniaux.  An Abstract Analysis of the Probabilistic Termination of Programs , 2001, SAS.

[98]  Rob J. van Glabbeek,et al.  Branching time and abstraction in bisimulation semantics , 1996, JACM.

[99]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[100]  David Monniaux,et al.  Abstract Interpretation of Probabilistic Semantics , 2000, SAS.

[101]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[102]  Robin Milner,et al.  An Algebraic Definition of Simulation Between Programs , 1971, IJCAI.

[103]  Patrice Godefroid,et al.  Model checking for programming languages using VeriSoft , 1997, POPL '97.

[104]  Annabelle McIver,et al.  Probabilistic Models for the Guarded Command Language , 1997, Sci. Comput. Program..

[105]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[106]  Reinhard Wilhelm,et al.  Parametric shape analysis via 3-valued logic , 1999, POPL '99.