Monadic second-order definable graph transductions: a survey
Theoretical Computer Science - Selected papers of the 17th Colloquium on Trees in Algebra and Programming (CAAP '92) and of the European Symposium on Programming (ESOP), Rennes, France, Feb. 1992
Algebraic and Automata-Theoretic Properties of Formal Languages
Algebraic and Automata-Theoretic Properties of Formal Languages
On Infinite Transition Graphs Having a Decidable Monadic Theory
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A Short Introduction to Infinite Automata
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
On the Recognizability of Arrow and Graph Languages
ICGT '08 Proceedings of the 4th international conference on Graph Transformations
On equivalent representations of infinite structures
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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A natural way to describe a family of languages is to use rational transformations from a generator. From these transformations, Ginsburg and Greibach have defined the Abstract Family of Languages (AFL). Infinite graphs (also called infinite automata) are natural tools to study languages. In this paper, we study families of infinite graphs that are described from generators by transformations preserving the decidability of monadic second order logic. We define the Abstract Family of Graphs (AFG). We show that traces of AFG are rational cones and traces of AFG that admit a rationally colored generator are AFL. We generalize some properties of prefix recognizable graphs to AFG. We apply these tools and the notion of geometrical complexity to study subfamilies of prefix recognizable graphs.