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Commutative properties in formal languages pose problems at the frontier of computer science, computational linguistics and computational group theory. A prominent problem of this kind is the position of the language On, the language that contains the same number of letters ai and a¯i with 1⩽i⩽n, in the known classes of formal languages. It has rec...
Commutative properties in formal languages pose problems at the frontier of computer science, computational linguistics and computational group theory. A prominent problem of this kind is the position of the language $O_n$, the language that contains the same number of letters $a_i$ and $\bar a_i$ with $1\leq i\leq n$, in the known classes of forma...
We formulate a generalization of Petrov et al. (2006)'s split/merge algorithm for interpreted regular tree grammars (Koller and Kuhlmann, 2011), which capture a large class of grammar formalisms. We evaluate its effectiveness empirically on the task of discontinuous constituent parsing with two mildly context-sensitive grammar formalisms: linear co...
We explore the concept of hybrid grammars, which formalize and generalize a range of existing frameworks for dealing with discontinuous syntactic structures. Covered are both discontinuous phrase structures and non-projective dependency structures. Technically, hybrid grammars are related to synchronous grammars, where one grammar component generat...
We develop the concept of weighted aligned hypergraph bimorphism where the weights may, in particular, represent probabilities. Such a bimorphism consists of an R 0-weighted regular tree grammar, two hypergraph algebras that interpret the generated trees, and a family of alignments between the two interpretations. Semantically, this yields a set of...
The tree languages of tree-adjoining grammars are precisely those of linear monadic context-free tree grammars. Unlike the original proof, we present a direct transformation of a tree-adjoining grammar into an equivalent linear monadic context-free tree grammar.
Formula simplification is important for the performance of SAT solvers. However, when applied until completion, powerful preprocessing techniques like variable elimination can be very time consuming. Therefore, these techniques are usually used with a resource limit. Although there has been much research on parallel SAT solving, no attention has be...