Despite of being quite similar (agreement) problems, 1-set agreement (consensus) and general k-set agreement require surprisingly different techniques for proving the impossibility in asynchronous systems with crash failures: Rather than the relatively simple bivalence arguments as in the impossibility proof for consensus in the presence of a single crash failure, known proofs for the impossibility of k-set agreement in shared memory systems with f >= k > 1 crash failures use algebraic topology or a variant of Sperner's Lemma. In this paper, we present a generic theorem for proving the impossibility of k-set agreement in various message passing settings, which is based on a reduction to the consensus impossibility in a certain subsystem resulting from a partitioning argument.
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having po ...
Viktor Kuncak, Simon Guilloud, Sankalp Gambhir