Advances in Distributed Systems and Formal Methods

The field of distributed systems and formal methods is witnessing significant developments, with a focus on achieving arbitration-free consistency and exploring new algebraic and topological frameworks. Researchers are working towards unifying and generalizing previous results, revealing fundamental properties that delineate coordination-free consistency from inherently synchronized behavior. Notable papers in this area include: AFC theorem, which shows that an object specification within a consistency model admits an available implementation if and only if it is arbitration-free. The Singularity Theory of Concurrent Programs, which introduces a novel paradigm for the analysis and verification of concurrent programs using topological characterization and detection of deadlocks and livelocks.

Sources

Arbitration-Free Consistency is Available (and Vice Versa)

On Reduction and Synthesis of Petri's Cycloids

A Perspective on the Algebra, Topology, and Logic of Electrical Networks

Kleene Algebrae, Kleene Modules, and Morita Equivalence

The Singularity Theory of Concurrent Programs: A Topological Characterization and Detection of Deadlocks and Livelocks

Systems of Graph Formulas and their Equivalence to Alternating Graph Automata

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