Maurice Tutor

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Category > Computer Science Posted 17 Sep 2017 My Price 8.00

single numerical identifier

The grammar in Fig. 4.7 generates declarations for a single numerical identifier; these declarations involve four different, independent properties of numbers.

width=

a) Generalize the grammar of Fig. 4.7 by allowing n options Ai, for some fixed n and for i = 1,2 . . . , n, where Ai can be either ai or bi. Your grammar should use only O(n) grammar symbols and have a total length of productions that is O(n) .

b)   The grammar of Fig. 4.7 and its generalization in part (a) allow declarations that are contradictory and/or redundant, such as:

Declare  foo real  fixed real  floating

We could insist that the syntax of the language forbid such declarations; that is, every declaration generated by the grammar has exactly one value for each of the n options. If we do, then for any fixed n there is only a finite number of legal declarations. The language of legal declarations thus has a grammar (and also a regular expression), as any finite language does. The obvious grammar, in which the start symbol has a production for every legal declaration has n! productions and a total production length of O(n x n!). You must do better: a total production length that is

0 (n2n).

c)  Show that any grammar for part (b) must have a total production length of at least 2n.

d) What does part (c) say about the feasibility of enforcing non redundancy and non contradiction among options in declarations via the syntax of the programming language?

Answers

Maurice Tutor
(5)
Status NEW Posted 17 Sep 2017 02:09 PM My Price 8.00

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