Quantitative Analysis of Probabilistic Lossy Channel Systems

Many protocols are designed to operate correctly even in the case where the underlying communication medium is faulty. To capture the behaviour of such protocols, lossy channel systems (LCS) [3] have been proposed. In an LCS the communication channels are modelled as FIFO buffers which are unbounded, but also unreliable in the sense that they can nondeterministically lose messages. Recently, several attempts [5,1,4,6] have been made to study Probabilistic Lossy Channel Systems (PLCS) in which the probability of losing messages is taken into account and the following qualitative model checking problem is investigated: to verify whether a given property holds with probability one. Here we consider a more challenging problem, namely to calculate the probability by which a certain property is satisfied. Our main result is an algorithm for the following Quantitative model checking problem: Instance: A PLCS, its state s, a finite state ω-automaton A, and a rational θ > 0. Task: Find a rational r such that the probability of the set of computations that start at s and are accepted by A is between r and r + θ.

[1]  Parosh Aziz Abdulla,et al.  Verification of Probabilistic Systems with Faulty Communication , 2003, FoSSaCS.

[2]  Parosh Aziz Abdulla,et al.  Reasoning about Probabilistic Lossy Channel Systems , 2000, CONCUR.

[3]  Alain Finkel,et al.  Unreliable Channels are Easier to Verify Than Perfect Channels , 1996, Inf. Comput..

[4]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[5]  李幼升,et al.  Ph , 1989 .

[6]  Moshe Y. Vardi.  Probabilistic Linear-Time Model Checking: An Overview of the Automata-Theoretic Approach , 1999, ARTS.

[7]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

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

[9]  Christel Baier,et al.  Establishing Qualitative Properties for Probabilistic Lossy Channel Systems: An Algorithmic Approach , 1999, ARTS.

[10]  S. Purushothaman Iyer,et al.  Probabilistic Lossy Channel Systems , 1997, TAPSOFT.

[11]  J. Kemeny,et al.  Denumerable Markov chains , 1969 .

[12]  Parosh Aziz Abdulla,et al.  Verifying programs with unreliable channels , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[13]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[14]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[15]  Nathalie Bertrand,et al.  Model Checking Lossy Channels Systems Is Probably Decidable , 2003, FoSSaCS.

[16]  Philippe Schnoebelen,et al.  The Verification of Probabilistic Lossy Channel Systems , 2004, Validation of Stochastic Systems.

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

[18]  Parosh Aziz Abdulla,et al.  Undecidable Verification Problems for Programs with Unreliable Channels , 1994, Inf. Comput..

[19]  J. Esparza,et al.  Model checking probabilistic pushdown automata , 2004, LICS 2004.

[20]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[21]  Philippe Schnoebelen,et al.  Verifying lossy channel systems has nonprimitive recursive complexity , 2002, Inf. Process. Lett..