Tree-to-Graph Transductions with Scope

High-level natural language processing requires formal languages to represent semantic information. A recent addition of this kind is abstract meaning representations. These are graphs in which nodes encode concepts and edges relations. Node-sharing is common, and cycles occur. We show that the required structures can be generated through the combination of (i) a regular tree grammar, (ii) a sequence of linear top-down tree transducers, and (iii) a fold operator that merges selected nodes. Delimiting the application of the fold operator to connected subgraphs gains expressive power, while keeping the complexity of the associated membership problem in polynomial time.

[1]  Danqi Chen,et al.  A Fast and Accurate Dependency Parser using Neural Networks , 2014, EMNLP.

[2]  Derek G. Corneil,et al.  Complexity of finding embeddings in a k -tree , 1987 .

[3]  Joost Engelfriet,et al.  The Equivalence of Bottom-Up and Top-Down Tree-to-Graph Transducers , 1998, J. Comput. Syst. Sci..

[4]  William Chesley Rounds Trees, transducers, and transformations , 1968 .

[5]  Jacob Andreas,et al.  Parsing Graphs with Hyperedge Replacement Grammars , 2013, ACL.

[6]  Philipp Koehn,et al.  Abstract Meaning Representation for Sembanking , 2013, LAW@ACL.

[7]  Joost Engelfriet,et al.  Tree Automata and Tree Grammars , 2015, ArXiv.

[8]  Brenda S. Baker,et al.  Tree Transducers and Tree Languages , 1978, Inf. Control..

[9]  Bruno Courcelle,et al.  Monadic Second-Order Definable Graph Transductions: A Survey , 1994, Theor. Comput. Sci..

[10]  Alexander Koller Semantic construction with graph grammars , 2015, IWCS.

[11]  Christoph Teichmann,et al.  Graph parsing with s-graph grammars , 2015, ACL.

[12]  Richard M. Schwartz,et al.  Fast and Robust Neural Network Joint Models for Statistical Machine Translation , 2014, ACL.

[13]  Christopher D. Manning Part-of-Speech Tagging from 97% to 100%: Is It Time for Some Linguistics? , 2011, CICLing.

[14]  Annegret Habel,et al.  Hyperedge Replacement, Graph Grammars , 1997, Handbook of Graph Grammars.

[15]  Walter S. Brainerd,et al.  The Minimalization of Tree Automata , 1968, Inf. Control..

[16]  Giorgio Satta,et al.  Weighted DAG Automata for Semantic Graphs , 2017, CL.

[17]  Clemens Lautemann,et al.  Tree Automata, Tree Decomposition and Hyperedge Replacement , 1990, Graph-Grammars and Their Application to Computer Science.

[18]  Kevin Knight,et al.  DAGGER: A Toolkit for Automata on Directed Acyclic Graphs , 2012, FSMNLP.