Assignment 3

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Portland Community College *

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464

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Computer Science

Date

Nov 24, 2024

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pdf

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Uploaded by ProfessorIceCat10

Section 3.1: 1) Create a nfa for Σ = {a, b} that accepts the language L(ab* + (ab)*). Explanation: The NFA for L(ab* + (ab)*) consists of four states: q0, q1, q2, and q3, where q0 is the initial state, and q1 and q3 are the final states. Strings matching ab* will be accepted by state q1, while strings matching (ab)* will be accepted by q3. NFA: Test Cases: 2) Create a regular expression for the set of all strings that consist of an even number of 'a's followed by 'b' (for example "aab", "aaaab", "aaaaaab", etc.). To create a regular expression for strings that consist of an even number of 'a's followed by 'b', the regular expression will be: (aa)*b Explanation: (aa)*: Matches zero or more occurrences of 'aa', representing an even number of 'a's.

( b): Matches a single 'b' at the end of the string. Putting it together, (aa)*b will match strings with an even number of 'a's followed by 'b'. Examples of matching strings include "aab", "aaaaaab", "aaaaaaaaaab", and so on. Section 3.2: 3) Use the construction in Theorem 3.1 to create an nfa that accepts the language L(bb* + aba). Explanation: The NFA for L(bb* + aba) consists of five states: q0, q1, q2, q3, and q4, where q0 is the initial state, and q1 and q4 are the final states. Strings matching bb* will be accepted by state q1, while strings matching (aba) will be accepted by q4. NFA: Test Cases:

4) Create a regular expression for the language accepted by the following nfa: states: {q0,q1,q2,q3} input alphabet: {a,b} initial state: q0 final states: {q2} transitions: δ(q3,b) = {q2} δ(q1,b) = {q1} δ(q1,λ) = {q2} δ(q1,a) = {q2} δ(q0,b) = {q3,q1} NFA: Test Cases: Regular Expression: bb*(a+λ)+bb Explanation: The regular expression bb*(a+λ)+bb matches strings that start with one or more 'b's, followed by either an 'a' or nothing, or accept the strings "bb".

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Section 3.3: 5) Create an nfa for Σ = {a, b} that accepts the language generated by the following right-linear grammar: S -> abbA|baB A -> aba|a B -> bB|b Regular Expression: (abb(aba+a))+(babb*) Explanation: The regular expression : (abb(aba+a))+(babb*) matches strings generated by the given right-linear grammar: 1. (abb(aba+a)): Matches strings starting with 'abb', followed by either 'aba' or 'a'. 2. (babb*): Matches strings starting with 'ba', followed by one or more 'b's. Putting it together, the regular expression matches strings generated by the grammar S -> abbA|baB A -> aba|a B -> bB|b

6) Construct a right-linear grammar for the language L((a + b)*). Grammar: S → aS | bS | λ Explanation: The right-linear grammar S → aS | bS | λ generates the language L((a + b)*), which consists of all strings over the alphabet {a, b}, including the empty string λ .

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