Abstract Families of Graphs

Composition of Path Transductions

“…As proved in [17], such an (oriented) edge replacement may be simulated by using only finite inverse substitution and product.…”

“…In [17], an abstract family of graphs (AFG) is defined as a graph family closed by inverse finite substitution and product by finite graphs. A full-AFG is an AFG which is also closed by inverse rational substitution.…”

“…We proposed the notion of path transduction which is a graph transformation. With this definition, the correspondence between the graph transformation and the language transformation becomes clearer than it is in [17]. The AFG and full-AFG defined in [17] may be respectively defined by closure under bounded and unbounded path transductions.…”

“…This article is the continuation of [17] which extended to infinite graphs the classical language theoretic notion of abstract family [11,12]. Many families of graphs, like higher order pushdown graphs [5], Petri nets transitions graphs or automatic graphs [3] can be characterized by using a common and restricted set of simple graph transformations from specific generating systems [18].…”

Families of automata characterizing context-sensitive languages

“…Precisely, the transition graphs of pushdown automata and prefix-recognizable graphs are defined from language theory. Recently, Urvoy extended the work of Ginsburg and Greibach [20] to define abstract families of graphs [22]. The connection between families of graphs and language theory is even deeper: they constitute an elegant characterization of families of languages.…”