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Chapter 13: Modeling Computation

Expert-verified
Discrete Mathematics and its Applications
Pages: 847 - 901
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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240 Questions for Chapter 13: Modeling Computation

  1. Construct nondeterministic finite-state automata that recognize each of these sets.

    Found on Page 887

  2. Construct a finite-state machine that changes every other bit, starting with the second bit, of an input string, and leaves the other bits unchanged.

    Found on Page 864

  3. a) Show that the grammar \({{\bf{G}}_{\bf{1}}}\) given in Example 6 generates the set\({\bf{\{ }}{{\bf{0}}^{\bf{m}}}{{\bf{1}}^{\bf{n}}}{\bf{|}}\,{\bf{m,}}\,{\bf{n = 0,}}\,{\bf{1,}}\,{\bf{2,}}\,...{\bf{\} }}\).

    Found on Page 856

  4. Construct a Turing machine with tape symbols \({\bf{0}}\),\({\bf{1}}\), and \({\bf{B}}\) that, given a bit string as input, replaces the first two consecutive \({\bf{1's}}\) on the tape with \({\bf{0 's}}\) and does not change any of the other symbols on the tape.

    Found on Page 898

  5. Determine whether the string 01001 is in each of these sets.

    Found on Page 875

  6. a) Define a finite-state automaton.

    Found on Page 900

  7. What set of strings with symbols in the set \(\left\{ {{\bf{0,1,2}}} \right\}\) is represented by the regular expression \(\left( 2 \right){\left( {{\bf{0}} \cup \left( {{\bf{12}}} \right)} \right)^{\bf{*}}}\)?

    Found on Page 901

  8. Determine whether each of these strings is recognized by the deterministic finite-state automaton in Figure 1.

    Found on Page 875

  9. Construct a finite-state machine for the log-on procedure for a computer, where the user logs on by entering a user identification number, which is considered to be a single input, and then a password, which is considered to be a single input. If the password is incorrect, the user is asked for the user identification number again.

    Found on Page 864

  10. Construct a derivation of \({{\bf{0}}^{\bf{2}}}{{\bf{1}}^{\bf{2}}}{{\bf{2}}^{\bf{2}}}\) in the grammar given in Example 7.

    Found on Page 856

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