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Chapter 8 Exercises Exercise 1 *Regular Language Describe the strings denoted by the regular language over the binary alphabet C = {0,1): . O(op)*l . (Oll>*l(Oll>(Oll) . 0*10* lo* lo* D Solution on page 177 Exercise 2 *Finite State Automaton Find the regular language over the binary alphabet C = {0,1) ac- cepted by the finite state automaton in Figure 8.1. D Solution on page 177 Exercise 3 *Turing Machine Of the class of recursively enumerable languages, there is an impor- tant subclass called recursive languages. A language L is defined to be recursive if there exists a Turing machine M that satisfies the following: EXERCISE BOOK The finite state automaton Figure 8.1. rn if the input w E L, then M eventually enters the halting state qXcept and accepts it; rn if w $! L, then M eventually enters the halting state q,,jeCt and rejects it; the set F of all final states of M is defined to be F = {qaCcept). 1 Prove that a recursive language is recursively enumerable. 2 Prove that if L is a recursive language, so is its complement z. D Solution on page 177 Exercise 4 *Graph Colorability I Given an undirected
Published: Jan 1, 2006
Keywords: Turing Machine; Complexity Theory; Polynomial Time Algorithm; Graph Colorability; Regular Language
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