Publication

Easy Impossibility Proofs for k-Set Agreement in Message Passing Systems

2011
Conference Papers

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/2e7223fe-9e17-4e0c-bc1c-ec704afba635

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2011
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2e7223fe-9e17-4e0c-bc1c-ec704afba635

About this result

Related concepts (25)

Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".

Message Passing Interface

Message Passing Interface (MPI) is a standardized and portable message-passing standard designed to function on parallel computing architectures. The MPI standard defines the syntax and semantics of library routines that are useful to a wide range of users writing portable message-passing programs in C, C++, and Fortran. There are several open-source MPI implementations, which fostered the development of a parallel software industry, and encouraged development of portable and scalable large-scale parallel applications.

Proof theory

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.

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