Transductions of dags and trees

Abstract

Directed acyclic graphs (dags) model derivations of phrasestructure grammars analogously to the way that trees model derivations of context-free grammars.In this paper we introduce translations of such dags which naturally extend the bottom-up tree translations. Composition results of these dag-to-tree transformations are studied. It is shown that every "recursively enumerable tree language" can be obtained from a recognizable dag language by such a transduction. Tree languages obtained from some subsets of recognizable dag languages by these transductions are investigated.

Graph automata

“…Subsets of smag(Σ ) are called pattern languages. Our patterns are analogous with the unsorted abstract dags of [18,19,5]. For another formalization see also [15].…”

“…Pattern automata have originated in [10], see also [21], and their basic properties are examined in [18,19] and [5] under the name of pdag automata. A pattern automaton is a structure…”

“…In order to model derivations of 0-type grammars, Kamimura and Slutzki studied automata on rooted pdags, i.e., planar, directed, acyclic graphs (cf. [18,19]). The automata considered by Bossut, Dauchet and Warin, work exactly in the same way except that they use pdags with an unbounded number of roots and that they control the sequences of initial and final states by rational languages of state words (cf [5]).…”

Generalising Tree Traversals to DAGs

“…There are some automata models that come close to our approach. However, they either cause recomputation in case of conflicting top-down state (instead of providing a resolution operator ⊕) [18,30], restrict themselves to bottom-up state propagation only [3,11,16], or assume that the in-degree of nodes is fixed for each node label [23,34]. Either approach is too restrictive for the application we have demonstrated in this paper.…”

Language Generation via DAG Transduction

“…Hyperedge Replacement Gram-mar (HRG; Ehrig et al, 1999). The other is DAG automata, originally studied by Kamimura and Slutzki (1982) and extended by Chiang et al (2018). In this paper, we study DAG transducers in depth, with the goal of building accurate, efficient yet robust natural language generation (NLG) systems.…”