How to prevent adjoining in TAGs and its impact on the Average Case Complexity

The introduction of the adjoining operation to context-free grammars comes at high costs: The worst case time complexity of (Earley, 1968) is O n 3 ¡ , whereas Tree Adjoining Grammars have O n 6 ¡ ((Schabes, 1990)). Thus, avoiding adjoining as far as possible seems to be a good idea for reducing costs (e.g.) address this problem more radically by restricting the adjoining operation of TAGs such that it is no context-sensitive operation anymore. The result is O n 3 ¡ worst case parseability which stems from TIG's context-freeness. However, to preserve TAG's mildly context-sensitiveness the adjoining operation must not be restricted in any way. Another solution would be simply to call the adjoining operation less frequently: The production of items directly depends on the fashion of the underlying grammar and often adjoining is used to make the grammar more comprehensible or more adequate to the linguistic phenomenon even if there would be simpler representations as, for instance, left-or right recursion. This abstract (1st) sketches a way of reducing item generation through grammar transformation by using Schema-TAGs (STAGs , as introduced by (Weir, 1987), where tree sets are enumerated by regular expressions) which in contrast to TIGs keeps weak equivalence and performs better than factoring as proposed by (Harbusch, Widmann and Woch, 1998), and (2nd) provides a proof of the average case time complexity of STAGs based on the proposed transformation. In the following, adressing of nodes occurs in the fashion of (Gorn, 1967), i.e. each node of a tree gets a unique number – beginning with zero – which preserves the structure of the tree. For example, 1¢ 2 points to the second daughter of the first daughter of a root node, and in grammar G 1 of Fig. 2,