Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
LACL '97 Selected papers from the Second International Conference on Logical Aspects of Computational Linguistics
Lambek Grammars Based on Pregroups
LACL '01 Proceedings of the 4th International Conference on Logical Aspects of Computational Linguistics
Fully lexicalized pregroup grammars
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Unidirectional Lambek Grammars in Polynomial Time
Theory of Computing Systems - Special Issue: Symposium on Computer Science; Guest Editors: Sergei Artemov, Volker Diekert and Alexander Razborov
A savateev-style parsing algorithm for pregroup grammars
FG'09 Proceedings of the 14th international conference on Formal grammar
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We study pregroup grammars with letter promotions $p^{(m)}\Rightarrow q^{(n)}$. We show that the Letter Promotion Problem for pregroups is solvable in polynomial time, if the size of p(n) is counted as |n|+1. In Mater and Fix [11], the problem is shown to be NP-hard, but their proof assumes the binary (or decimal, etc.) representation of n in p(n), which seems less natural for applications. We reduce the problem to a graph-theoretic problem, which is subsequently reduced to the emptiness problem for context-free languages. As a consequence, the following problems are in P: the word problem for pregroups with letter promotions and the membership problem for pregroup grammars with letter promotions.