Polypodic codes

Word and tree codes are studied in a common framework, that of polypodes which are sets endowed with a substitution like operation. Many examples are given and basic properties are examined. The code decomposition theorem is valid in this general setup

Graph automata

AbstractMagmoids satisfying the 15 fundamental equations of graphs, namely graphoids, are introduced. Automata on directed hypergraphs are defined by virtue of a relational graphoid. The closure properties of the so-obtained class are investigated, and a comparison is being made with the class of syntactically recognizable graph languages

Finitely presentable tree series

Tree height is known to be a non-recognizable series. In this paper, we detect two remarkable classes where this series belongs: that of polynomially presentable tree series and that of almost linearly presentable tree series. Both the above classes have nice closure properties, and seem to constitute the first levels of a tree series hierarchy which starts from the class of recognizable treeseries

Varieties of graphoids and Birkoff’s theorem for graphs

The algebraic structure of graphoids is used in order to obtain the wellknown Birkhoff’s theorem in the framework of graphs. Namely we establish a natural bijection between the class of Σ-graphoids and the class of strong congruences over GR(Σ, X), which is the free graphoid over the doubly ranked alphabet Σ and the set of variables X

An Introduction To Polypodic Structures

Pollypodes is an algebraic structure in between monoids and - a lg ebras having the advantages of both of them. Many objects of different nature such as words, trees, graphs, functions, etc, can be studied in common into the framework of polypodes

Picture codes

We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given