4) Write a regular expression that defines the language over {a,b,c}, consisting of all words that begin and end in a double 'c', contain at least one letter between the starting double 'c' and the ending double 'c', where b's must occur in groups of 2 or more, and each group of b's must be preceded by an 'a'.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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### Homework Assignments 1-4

1. (Only the visible portion is transcribed.)

4) **Write a regular expression** that defines the language over {a,b,c}, consisting of all words that begin and end in a double 'c', contain at least one letter between the starting double 'c' and the ending double 'c', where b's must occur in groups of 2 or more, and each group of b's must be preceded by an ‘a’.

5) **Write a regular expression** that defines the language over {a,b,c}, consisting of all words in which c's can only occur when an odd number of a's have been seen up to that point. So c’s can occur between the 1st and 2nd a’s, and between the 3rd and 4th a’s, but not between the 2nd and 3rd a’s (and so on).

6) **Proofs:** provide an argument for each answer. Make it as proof-like as you can.
   - a) For two regular languages L₁ and L₂, is L₁L₂ a proper subset of L₁ always, sometimes, or never?
   - b) Prove or disprove (true or false): The regular expression (a+b)*c describes the language consisting of all words which end in "c".

7) **Exercise 2.2.6a (p. 54)** - Keep in mind that when reading binary from left to right, each additional bit ...

*(Note: all assignments should be considered and detailed further as per course requirements.)*

---

**Explanation for Graphs or Diagrams:**

[Note: As no graphs or diagrams are visible in the image, there is no further explanation provided.]

---

**Additional Notes:** Ensure to check the course material for completing exercises from page 54 and for any diagrams or visual aids related to the context of the assignments.
Transcribed Image Text:### Homework Assignments 1-4 1. (Only the visible portion is transcribed.) 4) **Write a regular expression** that defines the language over {a,b,c}, consisting of all words that begin and end in a double 'c', contain at least one letter between the starting double 'c' and the ending double 'c', where b's must occur in groups of 2 or more, and each group of b's must be preceded by an ‘a’. 5) **Write a regular expression** that defines the language over {a,b,c}, consisting of all words in which c's can only occur when an odd number of a's have been seen up to that point. So c’s can occur between the 1st and 2nd a’s, and between the 3rd and 4th a’s, but not between the 2nd and 3rd a’s (and so on). 6) **Proofs:** provide an argument for each answer. Make it as proof-like as you can. - a) For two regular languages L₁ and L₂, is L₁L₂ a proper subset of L₁ always, sometimes, or never? - b) Prove or disprove (true or false): The regular expression (a+b)*c describes the language consisting of all words which end in "c". 7) **Exercise 2.2.6a (p. 54)** - Keep in mind that when reading binary from left to right, each additional bit ... *(Note: all assignments should be considered and detailed further as per course requirements.)* --- **Explanation for Graphs or Diagrams:** [Note: As no graphs or diagrams are visible in the image, there is no further explanation provided.] --- **Additional Notes:** Ensure to check the course material for completing exercises from page 54 and for any diagrams or visual aids related to the context of the assignments.
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