Coin Lemmas with Random Variables

Coin lemmas are a tool for decoupling probabilistic and nondeterministic arguments in the analysis of concurrent probabilistic systems. They have revealed to be fundamental in the analysis of randomized distributed algorithms, where the interplay between probability and nondeterminism has proved to be subtle and difficult to handle. We reformulate coin lemmas in terms of random variables obtaining a new collection of coin lemmas that is independent of the underlying computational model and of more general applicability to the study of concurrent nondeterministic probabilistic systems.

[1]  Isaac Saias,et al.  Proving probabilistic correctness statements: the case of Rabin's algorithm for mutual exclusion , 1992, PODC '92.

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

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

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

[5]  Michael Ben-Or,et al.  Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols , 1983, PODC '83.

[6]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[7]  Roberto Segala,et al.  Formal verification of timed properties of randomized distributed algorithms , 1995, PODC '95.

[8]  Roberto Segala,et al.  Verification of the randomized consensus algorithm of Aspnes and Herlihy: a case study , 2000, Distributed Computing.

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

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

[11]  Daniel Lehmann,et al.  On the advantages of free choice: a symmetric and fully distributed solution to the dining philosophers problem , 1981, POPL '81.

[12]  Michael Ben-Or,et al.  Another advantage of free choice (Extended Abstract): Completely asynchronous agreement protocols , 1983, PODC '83.

[13]  Roberto Segala,et al.  The Essence of Coin Lemmas , 1998, PROBMIV.

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