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Summary: On the Refinement of Liveness Properties of Distributed Systems1
Paul Attie
Department of Computer Science
American University of Beirut
paul.attie@aub.edu.lb
August 7, 2006
Abstract
We present a new approach for reasoning about liveness properties of distributed systems,
represented as automata. Our approach is based on simulation relations, and requires reasoning
only over finite execution fragments. Current simulation-relation based methods for reasoning
about liveness properties of automata require reasoning over entire executions, since they in-
volve a proof obligation of the form: if a concrete and abstract execution "correspond" via the
simulation, and the concrete execution is live, then so is the abstract execution.
Our contribution consists of (1) a formalism for defining liveness properties, (2) a proof
method for liveness properties based on that formalism, and (3) two expressive completeness
results: firstly, our formalism can express any liveness property which satisfies a natural "robust-
ness" condition, and secondly, our formalism can express any liveness property at all, provided
that history variables can be used.
To define liveness, we generalize the notion of a complemented-pairs (Streett) automaton
to an infinite state-space, and an infinite number of complemented-pairs. Our proof method
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