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Give state diagrams of DFAs recognizing the following
Chapter , Problem 1.6(choose chapter or problem)
Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is \(\{0,1\}\)}.
\(\begin{array}{l}\text{a. } \{w \mid w \text{ begins with a 1 and ends with a 0} \}\\ \text{b. } \{w \mid w \text{ contains at least three 1 s } \}\\ \text{c. } \{w \mid w \text{ contains the substring 0101 (i.e., } w=x 0101 y \text{ for some } x \text{ and } y \text{ ) } \}\\ \text{d. } \{w \mid w \text{ has length at least 3 and its third symbol is a 0} \}\\ \text{e. } \{w \mid w \text{ starts with 0 and has odd length, or starts with 1 and has even length } \}\\ \text{f. } \{w \mid w \text{ doesn't contain the substring 110}\\ \text{g. } \{w \mid \text{ the length of } w \text{ is at most 5} \}\\ \text{h. } \{w \mid w \text{ is any string except 11 and 111} \}\\ \text{i. } \{w \mid \text{ every odd position of } w \text{ is a 1} \}\\ \text{j. } \{w \mid w \text{ contains at least two 0 s and at most one 1} \}\\ \text{k. } \{\varepsilon, 0\}\\ \text{1. } \{w \mid w \text{ contains an even number of 0s, or contains exactly two 1s } \}\\ \text{m. The empty set}\\ \text{n. All strings except the empty string}\end{array}\)
Questions & Answers
QUESTION:
Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is \(\{0,1\}\)}.
\(\begin{array}{l}\text{a. } \{w \mid w \text{ begins with a 1 and ends with a 0} \}\\ \text{b. } \{w \mid w \text{ contains at least three 1 s } \}\\ \text{c. } \{w \mid w \text{ contains the substring 0101 (i.e., } w=x 0101 y \text{ for some } x \text{ and } y \text{ ) } \}\\ \text{d. } \{w \mid w \text{ has length at least 3 and its third symbol is a 0} \}\\ \text{e. } \{w \mid w \text{ starts with 0 and has odd length, or starts with 1 and has even length } \}\\ \text{f. } \{w \mid w \text{ doesn't contain the substring 110}\\ \text{g. } \{w \mid \text{ the length of } w \text{ is at most 5} \}\\ \text{h. } \{w \mid w \text{ is any string except 11 and 111} \}\\ \text{i. } \{w \mid \text{ every odd position of } w \text{ is a 1} \}\\ \text{j. } \{w \mid w \text{ contains at least two 0 s and at most one 1} \}\\ \text{k. } \{\varepsilon, 0\}\\ \text{1. } \{w \mid w \text{ contains an even number of 0s, or contains exactly two 1s } \}\\ \text{m. The empty set}\\ \text{n. All strings except the empty string}\end{array}\)
Step 1 of 6
I am going to draw the given DFAs recognizing the following languages. Yellow states are accepting states.