Exercise 1: Regular Expressions........... 20 marks
Regular Expressions Syntax: The + operator in regular expressions is used in some books to denote one or more applications of Kleene star. However, in other places, such as JFLAP, + denotes the alternation operator, equivalent to . For the purpose of this assignment, we follow JFLAP and use operator + to denote an alternation. In JFLAP, you can use λ or g to denote the empty string (see Preferences menu).
For parts (i) to (iii), please type each word on a new line. The notation wi wj denotes concatenation of words
wi and wj , and wr denotes the word obtained by reversing w.
(a) Let R1 = 1(1∗ + 2∗ )3∗ (2∗ + 3)1∗2(1 + 3)∗2∗ and R2 = 1∗3(2 + 3)∗2∗ (1 + 3)∗ (1 + 3)∗ be two regular expressions.
Whenever asked to provide words, these must be non-empty ones (and different if more than one).
(2 marks) [E1-Qa1.txt] Give two non-empty words w1 and w2 such that {w1, w2} ⊆ L(R1) ∩ L(R2).
(2 marks) [E1-Qa2.txt] Give two non-empty words w1 and w2 such that {w1, w2} ⊆ L(R1) L(R2).
(2 marks) [E1-Qa3.txt] Give two non-empty words w1 and w2 such that {w1, w2} ⊆ L(R2) L(R1).
(1 mark) [E1-Qa4.txt] Give a non-empty word w ∈ L(R1) such that w wr ∈ L(R1).
(1 mark) [E1-Qa5.txt] Give a non-empty word w ∈ L(R1) such that w wr g L(R1).
(1 mark) [E1-Qa6.txt] Give a regular expression R such that L(R) = L(R1) ∪ L(R2).
(3 marks) [E1-Qa7.txt] Give a regular expression R such that L(R) = L(R1) ∩ L(R2).
(b) Give regular expressions for the following languages.
(2 marks) [E1-Qb1.txt] L1 = {a3n+2bm+1 | n ≥ 1, m ≥ 0, m mod 2 = 1}.
(2 marks) [E1-Qb2.txt] L2 = L1, where L is the complement of L (assume alphabet Σ = {a, b}).
(2 marks) [E1-Qb3.txt] L = {w | w ∈{a, b}∗, |w | mod 3 = 2}, where |w | denotes the length of w.
(2 marks) [E1-Qb4.txt]
L = {bnw1 | n > 1, w1 ∈ (({a, c }∗ ∩ {a, b, c }∗ ) ({b}∗ ∪ {c }))} ∩ {w2c | w2 ∈ {a, b, c }∗}.
Exercise 2: Grammars............ 20 marks
Provide regular expressions for the following
(3 marks) [E2-Qa1.txt] Give a regular expression R such that L(R) = L(G1), where G1 is:
S → AcB
A → ac | bC | g
B → baB | caB | D C → bC | g
D → aD | b
(3 marks) [E2-Qa2.txt] Give a regular expression R such that L(R) = L(G2), where G2 is:
S → ACS | g
A → aA | bA | bB B → cB | g
C → bcC | acC | D D → bD | g
(2 marks) [E2-Qa3.txt] Give a regular expression R such that L(R) = L(G1) ∪ L(G2).
(2 marks) [E2-Qa4.txt] Give a regular expression R such that L(R) = L(G1) ∩ L(G2).
Let G3 = ({S }, {a, b}, Γ, S ) be a grammar, where the set of rules Γ is defined as follows:
S → aSbSa S → bSbSa S → aSbSb S → g
(4 marks) [E2-Qb1.txt] Does there exist a regular expression R such that L(R) = L(G3)? If it exists, provide such R; otherwise, simply put 0.
Let L = {c2n−1amc3b2m+1an | n, m > 0}.
(3 marks) [E2-Qc1.txt] Complete the following context-free grammar G such such L(G ) = L.
S → ccSa | < missing string >
A → aAbb | aBbb B → ccc
Provide the missing string as a single line in the given text file (e.g., if your response is xSSy, submit a file with a single line containing string "xSSy" (of course, without the quotes)).
(3 marks) [E2-Qc2.txt] Does there exist a regular expression, DFA, regular grammar or PDA over the alphabet Σ = a, b, c which is equivalent to the language L? (Answer the following question as a string of bits that translate to 1 for yes and 0 for no. For example, if your answer is “no, no, yes, no" give your response as 0010).
Exercise 3: Automata........ 25 marks
Answer the following questions based on the finite state automaton M1 present in the JFLAP file
FA-3.a.jK available in Assessments section of the course website. Assume alphabet Σ = {a, b, c, d, e, f }.
(2 marks) [E3-Qa1.txt] Give four strings of length 4 accepted by M1. Please type each string on a new
(2 marks) [E3-Qa2.txt] Give four strings of length 4 rejected by M1. Please type each string on a new
(4 marks) [E3-Qa3.txt] Give the language of this machine M1 as a regular
(2 marks) [E3-Qa4.jff] Remove any redundant states from M1 and adjust the transitions Give your answer as a .jff JFLAP file.
(4 marks) [E3-Qa5.jff] Create an automaton M2 (deterministic or non-deterministic) such that it accepts the language L1 where L1 = L(M1) L (aca + aba + bab)∗ (a(ba)∗ + c∗a) . Your machine should not accept words that are not in this Give your answer in a .jff JFLAP file.
Let L1 = {w | w ∈ {0, 1}∗, w does not contain the substring 101101}.
(4 marks) [E3-Qb1.jff] Give the DFA M3 where L(M3) = L1.
(3 marks) [E3-Qb2.txt] Give the regular expression R such that L(R) = L1.
Notation x, A/X means a transition where x is the input symbol being read, A is the symbol on top of the stack that is popped, and X is the symbol pushed onto the stack. Here, λ stands for the “empty” input and g stands for the “empty” stack symbol. Acceptance is by final state and empty stack.
(2 marks) [E3-Qc1.txt] Give 4 strings of length 11 over Σ that are accepted by PDA M4. Remember to type each string on a new
(2 marks) [E3-Qc2.txt] Give 4 strings of length 11 over Σ that are rejected by PDA M4. Remember to type each string on a new
50 Answers
62 Answers
DescriptionIn this final assignment, the students will demonstrate their ability to apply two majorconstructs of the C programming language – Functions and Arrays – to solve computationalproblems.Arrays provide a convenient way to store &
The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is anPath finding involves finding a path from A to B. Typically we want the path to have certain properties,such as being the shortest or to avoid going through certain obstacles. As the main aim is to thinkabout path finding, we focus on the common task
Develop a program to emulate a purchase transaction at a retail store. This program will have two classes, a LineItem class and a Transaction class. The LineItem class will represent an individualDevelop a program to emulate a purchase transaction at a retail store. Thisprogram will have two classes, a LineItem class and a Transaction class. TheLineItem class will represent an individual line item of merchandise that acustomer is purchasing.
SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:1 Project 1 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define: SeaPortProgram e
Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:1 Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define: SeaPortProgram e
The first programming project involves writing a program that parses, using recursive descent, a GUI definition language defined in an input file and generates the GUI that it defines. The grammar for this language is defined below:1Project 1The first programming project involves writing a program that parses, using recursive descent, a GUIdefinition language defined in an input file and generates the GUI that it defines. The grammar for thislanguage is defined below:gui ::= Wi
CMSC 335 Project SeaPort Solved Project 3 Introduction the SeaPort Project series For this set of projects for the course we wish to simulate some of the aspects of a number of Sea PortsCMSC 335 Project SolvedProject 3 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:
CMSC 335 Project 4 Solved SeaPort Introduction the SeaPort Project series For this set of projects for the course we wish to simulate some of the aspects of a number of Sea Ports Here are the classes and their instance variables we wish to defineProject 4 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define: SeaPortProgram ext
CMSC 451 Project 2 Solved The second project involves completing and extending the C++ program that evaluates statements of an expression language contained in the module 3 case studyProject 2 The second project involves completing and extending the C++ program that evaluates statements of an expression language contained in the module 3 case study. The statements of that expression language consist of an arithmetic expression f
CMSC 451 Project 1 Solved The first project involves benchmarking the behavior of Java implementations of one of the following sorting algorithms bubble sort selection sort insertion sort Shell sort, merge sort quick sort or heap sortCMSC 451 Project 1The first project involves benchmarking the behavior of Java implementations of one of thefollowing sorting algorithms, bubble sort, selection sort, insertion sort, Shell sort, merge sort,quick sort or heap sort. You must post your
The ready solutions purchased from Library are already used solutions. Please do not submit them directly as it may lead to plagiarism. Once paid, the solution file download link will be sent to your provided email. Please either use them for learning purpose or re-write them in your own language. In case if you haven't get the email, do let us know via chat support.
Get Free Quote!
269 Experts Online