We study the family of rational sets of words, called completely reducible and which are such that the syntactic representation of their characteristic series is completely reducible. This family contains, by a result of Reutenauer, the submonoids generated by bifix codes and, by a result of Berstel and Reutenauer, the cyclic sets. We study the closure properties of this family. We prove a resu...

DNS is one of the most important components of the Internet infrastructure. Unfortunately, it is known to be difficult to implement, and available implementations are difficult to configure correctly. DNS performance and availability often suffer from poor configuration which leads to unavailability or erroneous behavior of distributed systems that depend on DNS. The data structures of DNS are ...

The classical supervised pattern recognition problem is considered. A model of learning Boolean formulas is implemented. A new computational procedure for constructing quantitative non-reducible descriptors is suggested. The proposed procedure has a diminished number of computational operations with respect to the procedure for constructing non-reducible descriptors and allows incremental learn...

A graph is Y Y-reducible if it can be reduced to a vertex by a sequence of series-parallel reductions and Y Y-transformations. Terminals are distinguished vertices which cannot be deleted by reductions and transformations. In this paper we show that four-terminal planar graphs are Y Y-reducible when at least three of the vertices lie on the same face. Using this result we characterize Y Y-reduc...

Although this definition is open to decisive objections, most of which are not new, NCA is not yet dead. There are still those of us who ask, on the presupposition that NCA or something very similar is the correct analysis of dispositions, whether dispositions can explain their manifestations, or whether the bearers of nothing but dispositional properties can fill space, or whether colours are ...

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given, together with results on the vanishing of homology and cohomology.

Let IL be the set of all hereditary and additive properties of graphs. For P1,P2 ∈ IL, the reducible property R = P1 ◦ P2 is defined as follows: G ∈ R if and only if there is a partition V (G) = V1 ∪ V2 of the vertex set of G such that 〈V1〉G ∈ P1 and 〈V2〉G ∈ P2. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the dec...