Chapter 13: Q19RE (page 900)
What is an unsolvable decision problem? Give an example of such a problem.
The halting problem is an example of an insolvable problem while “a challenge with the property that there is no efficient algorithm exists that can solve all instances of the problem”.
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a) Construct a phrase-structure grammar for the set of all fractions of the form a/b, where a is a signed integer in decimal notation and b is a positive integer.
b) What is the Backus–Naur form for this grammar?
c) Construct a derivation tree for +311/17 in this grammar.
Find a phrase-structure grammar for each of these languages.
a) the set consisting of the bit strings 0, 1, and 11
b) the set of bit strings containing only 1s
c) the set of bit strings that start with 0 and end with 1
d) the set of bit strings that consist of a 0 followed by an even number of 1s.
a)Define a phrase-structure grammar.
b)What does it mean for a string to be derivable from a string wby a phrase-structure grammar G?
In Exercises 16–22 find the language recognized by the given deterministic finite-state automaton
Find the output generated from the input string 01110 for the finite-state machine with the state table in
a) Exercise 1(a).
b) Exercise 1(b).
c) Exercise 1(c).
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