The Caucal Hierarchy of Infinite Graphs in Terms of Logic and Higher-Order Pushdown Automata [chapter]

Arnaud Carayol, Stefan Wöhrle
2003 Lecture Notes in Computer Science  
In this paper we give two equivalent characterizations of the Caucal hierarchy, a hierarchy of infinite graphs with a decidable monadic second-order (MSO) theory. It is obtained by iterating the graph transformations of unfolding and inverse rational mapping. The first characterization sticks to this hierarchical approach, replacing the languagetheoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation. The second characterization is
more » ... ve. We show that the family of graphs of the Caucal hierarchy coincides with the family of graphs obtained as the ε-closure of configuration graphs of higher-order pushdown automata. While the different characterizations of the graph family show their robustness and thus also their importance, the characterization in terms of higher-order pushdown automata additionally yields that the graph hierarchy is indeed strict.
doi:10.1007/978-3-540-24597-1_10 fatcat:hfabghdqxvan5ne5axcsk65exu