<?xml version="1.0" standalone="yes"?>
<Paper uid="C92-4183">
  <Title>Uniform Recognition tbr Acyclic Context-Sensitive Grammars is</Title>
  <Section position="1" start_page="0" end_page="0" type="abstr">
    <SectionTitle>
Abstract
</SectionTitle>
    <Paragraph position="0"> Context-sensitive grammars in which each rule is of the forln aZfl - -~ (-*Tfl are acyclic if the associated context-free grammar with the rules Z ~ 3' is acyclic. The problem whether an intmt string is in the language generated by an acyclic context-sensitive grammar is NP-conlplete.</Paragraph>
    <Paragraph position="1"> Introduction One of the most well-known classifications of rewrite grammars is the Chomsky hierarchy.</Paragraph>
    <Paragraph position="2"> Grammars and languages ~Lre of type 3 (regular), type 2 (context-free), type 1 (context-sensitive) or of type 0 (unrestricted). It is easy to decide whether a string is in tile language generated by a regular or (:ontext-free gralntnar. For context-.free grammars input strings can be re(: ogmzed in a time that is polynomiM in the length of the input string as well as in the length of the grammar. Earley \[197(I\] ha.s shown a t)ound of O(\[GI2n a) where G is the size of the grammar and n the length of the inlmt string, l/.ecognilion for context-sensitive gralnmars is harder: it is PSPACE-complete \[Garey aaM Johnson, 1979\], referring to \[Kuroda, 1964\] and \[Karp, 1972 t.</Paragraph>
    <Paragraph position="3"> II.ecognition of type 0 hulguages is undccidat)le (see e.g. Lewis and Papadimitriou \[1981\]).</Paragraph>
    <Paragraph position="4"> The area between context-free grammars and context-sensitive grammars is interesting for two rea.sons. First, people have tried to describe natural languages with rewrite grammars. Context-free grammars do not seem powerfull enough to descrihe natural languages. Context-free grammars generate context-free languages. Natural *The author was sponsored by project NF 102/62-356 ('StructurM and Semantic Parallels in Natural Languages and Programming Languages'), flmded by the Netherlands Organization for the Advancement of l\[escarch (NWO).</Paragraph>
    <Paragraph position="5"> languages are probal)ly not context-free. The eounterexamples of sentences that caal not be described with a context-free grammar are always a bit artifieiah Very big subparts of nat-IlEal languages are context-free. A grammar for naturM languages has to be only a bit stronger than context-free. That's why we are interested in grammars that are between context-free and context-sensitive.</Paragraph>
    <Paragraph position="6"> The second perspective is the one of efficient proeessability, lu a context-free model, sentences can be processed ellMently. In a context-sensitive one, they can not. It is very interesting to know where the border lies: in which models sentences can be processed efficiently and in which ones they Call not'? In tile 60's and 70's, attempts have been made to put restrictions on context-sensitive grammars in order to generate context-fl-ee lmtguages. Exa:mples are Book \[1972\[, till)bard \[1974\] and Ginsburg aud Greibaeh \[1966 I. Baker \[1974\] has shown that these methods come down to tile same more or less. They all block the use of eontex~ to pass information through the string. Book \[1973\] gives ;m ow~rview of atteHtpts to generate context-flee languages with non-context-free grammars. How to restrict permutative grammars in order to generate context-free languages is described in MiLkkinen \[1985\].</Paragraph>
    <Paragraph position="7"> t'eters 3r. and Ritchie \[1973\] proposed a linguisticMly motivated chaatge in the definition of the notion grammar. Subsequent replacements in a string are relflaced by node admissibility constraints in the parse trees of sentences in a con(ext.-flee grammar. However, this formalism leads to generation of context-free 1,'mguages too.</Paragraph>
    <Paragraph position="8"> The approach of restricting gramlnaxs such that they generate context-tree languages does not seem interesting from the natural language perspective nor fi'o~l the efficiency perspective. Thc Acrl,:s DE COLING-92, NANTES, 23-28 AO()I 1992 1 1 5 7 ~ROC/ O: COI.ING 92 NnNIES, AUG. 23-28, 1992 oMy advantages of tlfis kind of restrictions lie in the possibilty to describe a context-free language in a different way, which may be easier for some purpose.</Paragraph>
    <Paragraph position="9"> Another argument agMnst blocking information \[/3aker, \] 974\] is the problem of unbounded dependencies. Unbounded dependencies are dependencies over an mlbounded distance. Wh-movcment is an examI)le of it. The number of unbounded dependencies in naturM hmguage is (almost) always restricted. Models that restrict the amount of information that can be sent seem to come closer to models of hummL language than models restrict the distance over wlfich information can be sent.</Paragraph>
    <Paragraph position="10"> In the 70's and 80's attention has shifted to the perspective of efficient processing. Context-sensitive grammars have been restricted so that complexity of recognition lies somewhere between 7)SPAC$ and T'. Book \[1978\] has shown that for linear time context-sensitive grammars recognition is NP-complete even for (some) fixed grammars. l~lrthermore there is a result that recognition for growing context-sensitive grammars is t)olynomial for tLxed grammars \[Dalflhaus and Warmuth, t986\]. This article also tries to define a border between nearly-eflicient and just-efficient nmdels.</Paragraph>
    <Paragraph position="11"> We can define the notions uniform (or universal) recognition and recognition for a fixed grammar as follows.</Paragraph>
  </Section>
class="xml-element"></Paper>