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<Paper uid="P84-1015">
  <Title>USES OF C-GP.APHS lil A PROTOTYPE FOR ALrFC~ATIC TRNLSLATION,</Title>
  <Section position="4" start_page="61" end_page="63" type="metho">
    <SectionTitle>
3. DEFINITION OF THE PROTOTYPE.
</SectionTitle>
    <Paragraph position="0"> The prototype consists of a model and a data structure. The model is essentially a generalization of a Transformational System (TS) analogous to ROBRA \[2\] and whose grammars are rewriting systems of c-graphs (RSC) \[4,5,6\]. Regarding data structure, we use c-graphs, 3.1A Transformational ~stem.</Paragraph>
    <Paragraph position="1"> This TS is a c-graph-~c-graph transducer. It is a &amp;quot;control&amp;quot; graph whose nodes are RSC and the arcs are labelled by conditions.</Paragraph>
    <Paragraph position="2"> A TS is a cycle free oriented graph, with  only one input and such that, CI) Each node is labelled with a RSC or &amp;nul. (2) &amp;nul has no successor.</Paragraph>
    <Paragraph position="3"> (3) Each grammar of the RSC has a transition scheme S or c (empty scheme).</Paragraph>
    <Paragraph position="4"> ~4) Arcs of the same initial node are ordered.  TS works heuristically. G~ven a c-graph gn as an input, it searches for the first path endin~ in &amp;nul. This fact implies that all of the transition schemes on the path were satisfied. Any scheme not satisfied provokes a search of a new path. For example, if $1 is satisfied, TS produces Gl(gn)=g 1 and it proceeds to calculate G2(G1(go))=g ~. IY S 4' is satisfied the system stops and produce~ g~. Otherwise, it backtracks to GI and tests S2.-If it is satisfied g\] is produced. Otherwise, it tests S3, etc.</Paragraph>
    <Section position="1" start_page="61" end_page="63" type="sub_section">
      <SectionTitle>
3.2 A REWRITING SYSTEM.
</SectionTitle>
      <Paragraph position="0"> Let us consider a simple example: let GR be the following grar~mar for syntactic analysis (without intending an example of linguistic value).</Paragraph>
      <Paragraph position="2"> As we can see, each rule has: a name (RI,R2, ...), a left side and a right side.</Paragraph>
      <Paragraph position="3"> The left side defines the geometricaI Form  and the condition that an actual seg must meet in order to be transformed. It is a c-graph scheme composed of two parts: the structural descriptor that defines the geometrical form and the condition (between slashes) that tests label information. The first part use &amp;quot;*&amp;quot; as an &amp;quot;element of structural description&amp;quot; in the first rule. It denotes the fact that no seg must be right-concatenated to g3+~2+g4. The right side defines the transformation to be done. It consists of a structural descriptor, similar to the one on the left side and a llst of label assignments (also between slashes) where for each new iabe\] we precise the values it takes; and for each old one, its possible modifications. A point ends the rule. Note the properties of an empty g: if g' is any c-graph, then g.g'=g and g+g'=g'.</Paragraph>
      <Paragraph position="4"> Let us analyze the phrase: &amp;quot;Ana lista la tira&amp;quot;. The representation in our formalism is G7. Morphological analysis produces G8. Note that a11 ambiguities are kept in the same structure in the form of para\]\]e\] arcs. The application of GR to G8 results in Gg, where each arc will be labelled with a c-tree with a possib\]e interpretation of G8 in grammar GR. The sequence of applications is R3, R6, RS, RI, R2, R4. The system stops when. no more rules are applicab\]e.</Paragraph>
      <Paragraph position="6"> Operations are divided in two classes: (1) those where the structure is taken as a whole (glo~ a\]) and (2) those that transform substructures (local), I. Global Operations.</Paragraph>
      <Paragraph position="7"> Concatenation and alternation have been defined above. These operations produce sequentlaI c-graphs and bundles respectively, as well as the polynomia\] writing of regular c-graphs.</Paragraph>
      <Paragraph position="8"> Expansion. This operation produces a bundle exp(G) from all the roads of a c-graph G. For example, expansion of GIO produces exp(G10)=(b.f)+ (c.d.f)+(c.e).</Paragraph>
      <Paragraph position="9">  Factorization. There are two kinds and their results may differ. Consider G11=a.b+a.c+d.e+d.f+ g.f+h.e. Left factorlzation produces G12=a.(b+c)+ d.(e+f)+g.f+h.e, and right factorization G13=a.b+ a. c+ (d+h). e+ (d+g). f.</Paragraph>
      <Paragraph position="10"> Arborization. This operation constructs a c-tree from a c-graph. There may be several kinds of c-trees that can be constructed but we search for a tree that keeps vertical and horizontal orders, i.e. one that codes the structure of the c-graph. An &amp;quot;and-or&amp;quot; (y-o) tree is well suited for this purpose. The result of the operation will be a c-graph with one and only one arc labelled by the and-or tree. For example, arb(G)=G14 (cf. Fig. 7). Note that the non-regular seg has ~ as a root.  3.3 Operations.</Paragraph>
      <Paragraph position="11"> 2. Local Operations.</Paragraph>
      <Paragraph position="12">  Replacement. Given two c-graphs G and G&amp;quot;,this operation substitutes a seg G' in G for G&amp;quot;, e.g. if G=G4, G&amp;quot;=m+n and G'=i, then the result will be  G 15=g+ (re+n) : (j+k).</Paragraph>
      <Paragraph position="13"> Addition. This operation inserts a c-graph G' into another, G, by merging two distinct nodes (x, y) of G with the input and output of G'. Addition requires only that insertion does not produce cycles. Note that if (I,0) are taken as a couple of nodes, we have alternation. Example, let (2,3) be a couple of nodes of G16 and take G'=G17=s+u. The resulting c-graph is G18.</Paragraph>
      <Paragraph position="14">  Erasing. This eliminates a substructure G' of a c-graph G. Erasing may destroy the structure even if we work with isolated seg's. Consequently, it is only defined on particular classes of seg's, namely segfi's and segmi's. For any other substructure, we eliminate the smaller segmi that contains it. A special case constitutes a segfi G' such that I and 0 do not belong to G'. Eliminating G' in such a case produces two non-connecting nodes in the c-graph that we have chosen to merge to preserve homogeneity. Example: let us take G and G'= GIO, then the result of erasing GIO from G is G19= G2.G4.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="63" end_page="63" type="metho">
    <SectionTitle>
4. IMPLEMENTATION.
</SectionTitle>
    <Paragraph position="0"> A small system has been programmed in PROLOG \[4\] (mainly operations) and in PASCAL (TS and RSC).</Paragraph>
    <Paragraph position="1"> For the first approach, we chose regular c-graphs to work with, since there is always a string to represent a c-graph of this class.</Paragraph>
    <Paragraph position="2"> In its present state, the system has two parts: (1) the Transformational System including the rewriting system and (2) the set of local and global operations.</Paragraph>
    <Paragraph position="3"> The TS is interactive. It consists of an analyzer that verifies the structure of the TS given as a console input and of the TS proper. As data we have the console input and a segment composed of transition schemes. There are no finer controls for different modes of grammar execution.</Paragraph>
    <Paragraph position="4"> Regarding operations and from a methodological point of vlew, algorithms for c-graph treatment can be divided in two classes: (I) the one where we search for substructures and (2) the one where this search is not needed. Obviously, local operations belong to the first class, but among global operations, only concatenation, alternation and expansion belong to the second one. Detailed description of algorithms of this part Of ~he system can be found in \[4\].</Paragraph>
  </Section>
  <Section position="6" start_page="63" end_page="63" type="metho">
    <SectionTitle>
5. CONCLUSION.
</SectionTitle>
    <Paragraph position="0"> Once we have an operational version of the prototype, it is intended as a first approach to proceed to the translation of assemblers of the microprocessors available in our laboratory such as INTEL's 8085 or 8080 and MOTOROLA's 6800.</Paragraph>
  </Section>
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