Parsing Pregroup Grammars with Letter Promotions in Polynomial Time

Abstract

We consider pregroup grammars with letter promotions of the form $p^{(m)} \Longrightarrow q^{(n)}, p \Longrightarrow 1, 1 \Longrightarrow q$. We prove a variant of Lambek’s normalization theorem [5] for the calculus of pregroups enriched with such promotions and present a polynomial parsing algorithm for the corresponding pregroup grammars. The algorithm extends that from [8], elaborated for pregroup grammars without letter promotions. The normalization theorem, restricted to letter promotions without 1, was proved in [3,4] while the present version was stated in [4] without proof and used to show that the word problem for letter promotions with unit is polynomial. Our results are contained in the unpublished PhD thesis [9].