The equivalence of four extensions of context-free grammars
Mathematical Systems Theory
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Semilinearity as a Syntactic Invariant
LACL '96 Selected papers from the First International Conference on Logical Aspects of Computational Linguistics
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
Commutation-augmented pregroup grammars and push-down automata with cancellation
Information and Computation
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A family of languages is called mildly context-sensitive if - it includes the family of all ε-free context-free languages; - it contains the languages • {anbncn : n ≥ 1} - multiple agreement, • {ambncmdn : m, n ≥ 1} - crossed dependencies, and • {ww : w ∈ Σ+} - reduplication; - all its languages are semi-linear; and - their membership problem is decidable in polynomial time. In our paper we introduce a new model of computation called buffer augmented pregroup grammars that defines a family of mildly contextsensitive languages. This model of computation is an extension of Lambek pregroup grammars with a variable symbol - the (buffer) and is allowed to make an arbitrary substitution from the original pregroup to the variable. This increases the pregroup grammar generation power, but still retains the desired properties of mildly context-sensitive languages such as semi-linearity and polynomial parsing. We establish a strict hierarchy within the family of mildly context-sensitive languages defined by buffer augmented pregroup grammars. In this hierarchy, the hierarchy level of the family language depends on the allowed number of occurrences of the variable in lexical category assignments.