A Linear LAG for ai ! Markus Schulze Department of Computational Linguistics

The mainstream of syntax analysis has been discussing the question of mathematical complexity of natural language parsingmostly in relation to the well-known Chomsky-hierarchy. There are however other grammar models with different complexity-hierarchies that are worth looking at. This paper presents a grammar for ai! that parses with linear complexity in a non-PSGformalism, while a PSG for this language would have exponential complexity. The underlying grammar formalism used here is the left-associative grammar (LAG), which is based on the principle of possible continuations. In contrast to conventional LAGs with a category consisting of one double-ended queue (deque), the grammar presented here, uses three deques. Accordingly it is shown how the complexity class of a LAG with n deques can be found. This is done with essentially the same criteria as it is done when discussing single-deque LAGs.