A General Constructive Proof Technique

A constructive proof for FLP

We present a simple elementary proof for the result of Fischer, Lynch, and Paterson (FLP) [J. ACM 32 (2) (April 1985) 374–382] that the consensus problem cannot be solved deterministically in an asynchronous system where a single process may fail by crashing. Our proof is, in contrast to the original, constructive in its crucial lemma, showing not only that a nonterminating execution does exist...

Deriving SN from PSN: a general proof technique

In the framework of explicit substitutions there is two termination properties: preservation of strong normalization (PSN), and strong normalization (SN). Since there are not easily proved, only one of them is usually established (and sometimes none). We propose here a connection between them which helps to get SN when one already has PSN. For this purpose, we formalize a general proof techniqu...

A General Technique for Analyzing Termination in Symmetric Proof Calculi

Proof-term calculi expressing a computational interpretation of classical logic serve as tools for extracting the constructive content of classical proofs and at the same time can be seen as pure programming languages with explicit representation of control. The inherent symmetry in the underlying logic presents technical challenges to the study of the reduction properties of these systems. We ...

A Constructive Proof of Gleason's Theorem

A Constructive Proof of Vizing's Theorem

We consider finite graphs with no self-loops and no multiple edges. A graph is valid if all edges incident on a vertex have different colors. We prove Vizing’s Theorem. All the edges of a graph of maximum degree less than N can be colored using N colors so that the graph is valid. We call a color incident on a vertex if an edge incident on that vertex has that color; otherwise, the color is fre...