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<Paper uid="E93-1042">
  <Title>NEW FRONTIERS BEYOND CONTEXT-FREENESS: DI-GRAMMARS AND DI-AUTOMATA.</Title>
  <Section position="3" start_page="0" end_page="358" type="metho">
    <SectionTitle>
I Introduction
</SectionTitle>
    <Paragraph position="0"> It is common practice to parse nested Wh-dependencies, like the classical example of Rizzi (1982) in (1), (1) Tuo fratello, \[a cui\]l mi domando \[che storie\]2 abbiano raccontato t 2 t 1, era molto preoccupato (Your Brother, \[to whom\] 1 I wonder \[which stories\] 2 they told t 2 t 1 was very troubled) using a stack mechanism. Under the binary branching hypothesis the relevant structure of (1) augmented by wh-stacks is as follows: (2) \[a cui\] 1 mi dornando Lpush ---tit 11--~ i--push ---~\[t2,tll--- 1 \[che storie\]2abbiano V2\[t2,tl\] / \</Paragraph>
    <Paragraph position="2"> Up to now it is unclear, how far beyond context-freeness the generative power of a Type 2 grammar formalism is being extended if such a stack mechanism is grafted on it (assuming, of course, that an upper bound for the size of the stack can not be motivated).</Paragraph>
    <Paragraph position="3"> Fernando Pereira's concept of Extraposition Grammar (XG), introduced in his influential paper (Pereira, 1981; 1983; cf. Stabler, 1987) in order to delimit the new territory, can be shown to be inadequate for this purpose, since it is provable that the class of languages generable by XGs coincides with Type 0 (i,e. XGs have the power of Turing machines), whereas the increase of power by the stack mechanism is not even enough to generate all Type 1 languages (see below).</Paragraph>
    <Paragraph position="4"> In (2) an additional point is illustrated: the stack \[t2,tl\] belonging to V 2 has to be divided into the substacks \[t2\] and \[tl\], which are then inherited by the daughters V l and PP. For the PP-index tlis not discharged from the top of the V2-stack \[t2,tl\]. Generalizing to stacks of unlimited size, the partition of a stack among the inheriting subconstituents K 1 and K 2 of a constituent K 0 is as in (3)</Paragraph>
    <Paragraph position="6"> If the generalization in (3) is tenable, the extension of context-free grmnmars (Vijay-Shanker and Weir, 1991, call the resulting formalism &amp;quot;linear indexed granunar&amp;quot; (LIG)) discussed by Gazdar in (Gazdar, 1988), in which stacks are exclusively passed over to a single daughter (as in (3.1)), is too weak.</Paragraph>
    <Paragraph position="8"> Stack-transmission by distribution, however, as in (3) suggests the definition of a new class of grammars properly containing the context-free class.</Paragraph>
  </Section>
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