Second-Level Algorithms, Superrecursivity, and Recovery Problem in Distributed Systems

In this paper, we analyze network recovery algorithms, which allow computer networks to properly function in spite of failures. In this analysis, we use methods and tools of the theory of super-recursive algorithms. The concept of algorithm of the second level is introduced and studied. It is demonstrated that although the main components of various check-point/recovery algorithms are recursive algorithms, check-point/recovery algorithms, as a whole, are super-recursive second-level algorithms. Treating network recovery algorithms as second level algorithms is oriented at developing more powerful algorithms by combining existing ones in a common schema.