Automata on DAG representations of finite trees
Witold Charatonik · MPG.PuRe (Max Planck Society) · 1999
We introduce a new class of finite automata. They are usual bottom-up tree automata that run on DAG representations of finite trees. We prove that the emptiness problem for this class of automata is NP-complete. Using these automata we prove the decidability of directional type checking for logic programs, and thus we improve earlier results by Aiken and Lakshman. We also show an application of these automata in solving systems of set constraints, which gives a new view on the satisfiability problem for set constraints with negative constraints. Keywords Tree Automata, Directed Acyclic Graphs, Types in Logic Programming, Semantics of Logic Programs, Set Constraints 1 Introduction We introduce a new class of finite automata, which we call automata on t-dags. They are usual bottom-up tree automata that run on DAG representations of ground terms over given signature. The class of languages recognizable by these automata contains all DAG representations of regular sets of terms...