313F04M - CPSC 313 Midterm Test November 4, 2004 Name:...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
CPSC 313 — Midterm Test November 4, 2004 Name: Lecture Section: Lab Section: Please DO NOT write your ID number on this page. Instructions: Answer all multiple choice questions in part B on the score card using pencil . Answer all questions in part A in the space provided. No Aids Allowed. There are a total of 52 marks available on this exam. The exam will be marked out of 48. Duration: 120 minutes
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ID Number: Section Question Score Possible score A 1 5 2 5 3 5 4 5 5 2 6 5 7 5 B 1-20 20 Total: 48 (+ 4 bonus marks) 1
Background image of page 2
ID Number: Part A - Short Answer Answer all open ended questions in this section in the space provided. At the end of this exam booklet some additional space is provided if needed. Make sure you indicate clearly where the answer to a question is located. The amount of marks each question is worth is indicated with the question. 1. [5 marks] Draw a transition diagram for a finite automaton that accepts the language L 1 = { w ∈ { 0 , 1 } * | w has odd length and ends with 11 } Briefly explain why your finite automata is correct. 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ID Number: 2. [5 marks] Consider the deterministic finite automaton (DFA) M 2 which processes string over the alphabet Σ = { a,b,c } and whose transition diagram is as follows. q 0 q 1 q 2 start a,b c a,b c a,b,c Prove that, for any string w Σ * , b δ ( q 0 ,w ) = q 0 if and only if w ∈ { a,b } * . 3
Background image of page 4
ID Number: 3. [5 marks] Use the closure properties for regular languages to prove that the language L 3 = { wcw | w ∈ { a,b } * } is not a regular language. In your proof, you may use the fact that the language L 0 = { ww | w ∈ { a,b } * } is not a regular language. 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ID Number: 4. [5 marks] Give a regular expression whose language is L 4 = { w ∈ { a,b,c } * | w contains at least 1 a and at least 1 c } Explain why your answer is correct. 5. [2 marks] Consider the context-free grammar G 5 = ( V,T,P,S ) where V = { S,A,B } , T = { a,b } and P contains the rules S AbB A AA | a | ± B BB | a | b | ± Show that the grammar G 5 is ambiguous. 5
Background image of page 6
ID Number: 6. [5 marks] Consider again the context-free grammar G 5 from the previous question. We can prove the following claims: Claim 1 w T * B * G 5 w if and only if w L B = T * .
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 13

313F04M - CPSC 313 Midterm Test November 4, 2004 Name:...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online