Global State Estimates for Distributed Systems

We consider distributed systems modeled as communicating finite state machines with reliable unbounded FIFO channels. As an essential sub routine for control, monitoring and diagnosis applications, we provide an algorithm that computes, during the execution of the system, an estimate of the current global state of the distributed system for each local subsystem. This algorithm does not change the behavior of the system; each subsystem only computes and records a symbolic representation of the state estimates, and piggybacks some extra information to the messages sent to the other subsystems in order to refine their estimates. Our algorithm relies on the computation of reachable states. Since the reachability problem is undecidable in our model, we use abstract interpretation techniques to obtain regular overapproximations of the possible FIFO channel contents, and hence of the possible current global states. An implementation of this algorithm provides an empirical evaluation of our method.

[1]  R. Kumar,et al.  Distributed state estimation in discrete event systems , 2009, 2009 American Control Conference.

[2]  Thierry Massart,et al.  A Calculus to Define Correct Tranformations of LOTOS Specifications , 1991, FORTE.

[3]  Daniel Brand,et al.  On Communicating Finite-State Machines , 1983, JACM.

[4]  Benoît Caillaud,et al.  Mind the gap: Expanding communication options in decentralized discrete-event control , 2007, 2007 46th IEEE Conference on Decision and Control.

[5]  Stéphane Lafortune,et al.  Coordinated Decentralized Protocols for Failure Diagnosis of Discrete Event Systems , 2000, Discret. Event Dyn. Syst..

[6]  Stéphane Lafortune,et al.  Minimal Communication for Essential Transitions in a Distributed Discrete-Event System , 2007, IEEE Transactions on Automatic Control.

[7]  Friedemann Mattern,et al.  Virtual Time and Global States of Distributed Systems , 2002 .

[8]  Pierre Wolper,et al.  The Power of QDDs , 1997 .

[9]  Peter Bro Miltersen,et al.  SOFSEM 2009: Theory and Practice of Computer Science, 35th Conference on Current Trends in Theory and Practice of Computer Science, Spindleruv Mlýn, Czech Republic, January 24-30, 2009. Proceedings , 2009, SOFSEM.

[10]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[11]  Paul Gastin,et al.  Natural Specifications Yield Decidability for Distributed Synthesis of Asynchronous Systems , 2009, SOFSEM.

[12]  Vincent Danos,et al.  Transactions in RCCS , 2005, CONCUR.

[13]  Leslie Lamport,et al.  Time, clocks, and the ordering of events in a distributed system , 1978, CACM.

[14]  Gérard Berry,et al.  The Esterel Synchronous Programming Language: Design, Semantics, Implementation , 1992, Sci. Comput. Program..

[15]  Stéphane Lafortune,et al.  Coordinated decentralized protocols for failure diagnosis of discrete event systems , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[16]  L. Helouet,et al.  Diagnosis from scenarios [system diagnosis] , 2006, 2006 8th International Workshop on Discrete Event Systems.

[17]  Stéphane Lafortune,et al.  Failure diagnosis using discrete event models , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[18]  Pierre Wolper,et al.  The Power of QDDs (Extended Abstract) , 1997, SAS.

[19]  Blaise Genest,et al.  On Implementation of Global Concurrent Systems with Local Asynchronous Controllers , 2005, CONCUR.

[20]  Grégoire Sutre,et al.  Extrapolation-Based Path Invariants for Abstraction Refinement of Fifo Systems , 2009, SPIN.

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

[22]  Bertrand Jeannet,et al.  Verification of Communication Protocols Using Abstract Interpretation of FIFO Queues , 2006, AMAST.

[23]  Alain Finkel,et al.  Well-abstracted transition systems: application to FIFO automata , 2003, Inf. Comput..

[24]  Ahmed Bouajjani,et al.  Symbolic Reachability Analysis of FIFO-Channel Systems with Nonregular Sets of Configurations , 1999, Theor. Comput. Sci..

[25]  Andreas Podelski,et al.  ACSAR: Software Model Checking with Transfinite Refinement , 2007, SPIN.