Uniform parsing for hyperedge replacement grammars

Parsing Weighted Order-Preserving Hyperedge Replacement Grammars

“…Rooted subgraphs are strictly nested, which is proved by Björklund et al (2018) in the form of the following lemma (where ∼ is isomorphy modulo the order of g ):…”

“…A HRG is reentrancy preserving if it has only reentrancy-preserving rules. We note here that Björklund et al (2018) also permits chain rules, i.e. rules that only change the label of an edge from one nonterminal to another nonterminal, and thus violate the first condition above.…”

“…when the grammar is considered to be part of the input. Here, we define a weighted version of OPHGs, and extend the results of Björklund et al (2018) to show that when the weights are taken from a commutative semiring, we can efficiently compute the weight assigned by an OPHG to any input graph. This is an important feature since applications such as semantic modelling require ways to quantify the well-formedness of a generated graph.…”

“…Thus, from both perspectives less powerful special cases should be sought if this helps to cut down on parsing complexity. Recently, such a restriction, called order preservation, was proposed and studied in (Björklund et al, 2016;Björklund et al, 2017;Björklund et al, 2018).…”

“…The present article builds upon the orderpreserving HRGs (OPHGs) of Björklund et al (2018), where it was shown that parsing for OPHGs is efficient, requiring polynomial time even in the uniform case i.e. when the grammar is considered to be part of the input.…”