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Show a possibly NFA to accept each of the following languages: a) {a"ba" | n, m 2 0} b) {we {a, b} *: w contains at least one instance of aaba, bbb or ababa} c) {w e {0, 1*: w corresponds to the binary encoding of a positive integer that is div

Show a possibly NFA to accept each of the following languages: a) {a"ba" | n, m 2 0} b) {we {a, b} *: w contains at least one instance of aaba, bbb or ababa} c) {w e {0, 1*: w corresponds to the binary encoding of a positive integer that is div

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Non-deterministic Finite Automata (NFA) Design for Given Languages This section explores designing possibly non-deterministic finite automata (NFA) for each specified language: a) **Language: \( \{a^n b^m | n, m \geq 0\} \)** - **Description:** This language consists of strings that have any number of 'a' characters followed by any number of 'b' characters, including the empty string. - **NFA Design:** - An NFA for this language might have a start state that loops on receiving 'a', then transitions to another state that loops on receiving 'b'. This allows acceptance of strings like "", "a", "aaa", "ab", "aab", etc. b) **Language: \( \{w \in \{a, b\}^* | w \text{ contains at least one instance of aaba, bbb, or ababa}\} \)** - **Description:** This language accepts strings if they contain at least one occurrence of "aaba", "bbb", or "ababa". - **NFA Design:** - Construct separate paths leading to an accept state for the substrings "aaba", "bbb", and "ababa". This includes transitions that scan for each specific substring pattern amidst other characters. c) **Language: \( \{w \in \{0, 1\}^* | w \text{ corresponds to the binary encoding of a positive integer that is divisible by 16 or is odd}\} \)** - **Description:** This language considers binary strings that either represent a positive integer divisible by 16 or an odd integer. - **NFA Design:** - For divisibility by 16, the NFA should accept binary strings ending in four '0's with some non-zero prefix. - For odd integers, ensure acceptance if the string ends with '1'. Implement multiple paths to cater to both conditions, ensuring any valid ending moves to an accept state. This educational resource provides strategies for creating NFAs to accept specified languages, emphasizing logical transitions and state management for various string patterns and conditions.
Transcribed Image Text:### Non-deterministic Finite Automata (NFA) Design for Given Languages This section explores designing possibly non-deterministic finite automata (NFA) for each specified language: a) **Language: \( \{a^n b^m | n, m \geq 0\} \)** - **Description:** This language consists of strings that have any number of 'a' characters followed by any number of 'b' characters, including the empty string. - **NFA Design:** - An NFA for this language might have a start state that loops on receiving 'a', then transitions to another state that loops on receiving 'b'. This allows acceptance of strings like "", "a", "aaa", "ab", "aab", etc. b) **Language: \( \{w \in \{a, b\}^* | w \text{ contains at least one instance of aaba, bbb, or ababa}\} \)** - **Description:** This language accepts strings if they contain at least one occurrence of "aaba", "bbb", or "ababa". - **NFA Design:** - Construct separate paths leading to an accept state for the substrings "aaba", "bbb", and "ababa". This includes transitions that scan for each specific substring pattern amidst other characters. c) **Language: \( \{w \in \{0, 1\}^* | w \text{ corresponds to the binary encoding of a positive integer that is divisible by 16 or is odd}\} \)** - **Description:** This language considers binary strings that either represent a positive integer divisible by 16 or an odd integer. - **NFA Design:** - For divisibility by 16, the NFA should accept binary strings ending in four '0's with some non-zero prefix. - For odd integers, ensure acceptance if the string ends with '1'. Implement multiple paths to cater to both conditions, ensuring any valid ending moves to an accept state. This educational resource provides strategies for creating NFAs to accept specified languages, emphasizing logical transitions and state management for various string patterns and conditions.
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