[For the entire collection see Zbl 0643.00024.]
Directed acyclic graphs (dags) are used in the study of parallelism, relational data bases and unification algorithms. They are also used to model derivations of phrase-structure grammars. In this paper the authors study languages of planar dags (pdags). They introduce an appropriate “rational” language for specifying pdag languages as well as pdag recognizers. The latter extend dag automata studies by Kamimura and the reviewer. A Kleene-like result is proved that shows the equivalence of the rational specification language and the pdag automata.