<?xml version="1.0" standalone="yes"?>
<Paper uid="P96-1032">
  <Title>Efficient Tabular LR Parsing</Title>
  <Section position="3" start_page="239" end_page="239" type="intro">
    <SectionTitle>
2 Definitions
</SectionTitle>
    <Paragraph position="0"> Throughout this paper we use standard formal language notation. We assume that the reader is familiar with context-free grammar parsing theory (Harrison, 1978).</Paragraph>
    <Paragraph position="1"> A context-free grammar (CFG) is a 4-tuple G = (S, N, P, S), where S and N are two finite disjoint sets of terminal and nonterminal symbols, respectively, S E N is the start symbol, and P is a finite set of rules. Each rule has the form A ---* a with A E N and a E V*, where V denotes N U E. The size of G, written I G I, is defined as E(A--*a)EP \[Aot I; by I a I we mean the length of a string of symbols a.</Paragraph>
    <Paragraph position="2"> We generally use symbols A,B,C,... to range over N, symbols a, b, c,... to range over S, symbols X, Y, Z to range over V, symbols ~, 8, 7,... to range over V*, and symbols v, w, z,... to range over S*.</Paragraph>
    <Paragraph position="3"> We write e to denote the empty string.</Paragraph>
    <Paragraph position="4"> A CFG is said to be in binary form if ~ E {e} U V t.J N 2 for all of its rules A --* c~. (The binary form does not limit the (weak) generative capacity of context-free grammars (Harrison, 1978).) For technicM reasons, we sometimes use the augmented grammar associated with G, defined as G t = (St, N t, pt, St), where St, t&gt; and &lt;1 are fresh symbols, S t = SU {t&gt;,&lt;l}, N t = NU {S t } and pt = p U {S t ~ t&gt;S&lt;~}.</Paragraph>
    <Paragraph position="5"> A pushdown automaton (PDA) is a 5-tuple .4 = (Z, Q, T, qi,, q/in), where S, Q and T are finite sets of input symbols, stack symbols and transitions, respectively; qin E Q is the initiM stack symbol and q/i, E Q is the finM stack symbol. 1 Each transition has the form 61 ~-~ 62, where 61,82 E Q*, 1 &lt; 161 l, 1 &lt; 1621 &lt; 2, and z = e or z = a. We generally use symbols q, r, s,... to range over Q, and the symbol</Paragraph>
  </Section>
class="xml-element"></Paper>