Galois Connections for Flow Algebras

Abstract : We generalise Galois connections from complete lattices to flow algebras. Flow algebras are algebraic structures that are less restrictive than idempotent semirings in that they replace distributivity with monotonicity and dispense with the annihilation property; therefore they are closer to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras using Galois connections such that correctness of the analyses is preserved. The approach is illustrated for a mutual exclusion algorithm.
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Piotr Filipiuk, Michał Terepeta, Hanne Nielson, Flemming Nielson. Galois Connections for Flow Algebras. 13th Conference on Formal Methods for Open Object-Based Distributed Systems (FMOODS) / 31th International Conference on FORmal TEchniques for Networked and Distributed Systems (FORTE), Jun 2011, Reykjavik,, Iceland. pp.138-152, ⟨10.1007/978-3-642-21461-5_9⟩. ⟨hal-01583315⟩

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