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C++ Programming: From Problem Analysis to Program Design

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 6PE

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Consider a set S of strings defined recursively as follows:
Base case: AES (A is the empty string, i.e. "" in programming.)
• Recursive rules: if x = S and y = S then,
1. axb € S
2. xy Є S

(a) List at least 8 distinct strings that are in S. You must use each recursive rule at least twice.
(b) List at least 2 strings made up of only as and bs that are not in S.

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The following recursive definition of a set S over {a, b, c, d}. Basis: "", a, b, c E S. Recursive Step: If ax E S, then bax ES and cax E S. If bx € S, then cbx € S. If cx = S, then bax ES and bcx = S. If dx E S, then ddx E S. Closure: SE S only if it is a, b or c or it can be obtained from a, b or c using finitely many operations of the Recursive Step. a) What recursive step can be removed from the above definition and why? b) Derive from the definition of S that bcbc S. c) Explain why baa & S.
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