(a) In regular expression theory, a regular expression is a pattern that defines a set of strings over an alphabet. Regular expressions are commonly used in computer science and programming to perform various operations such as searching, matching, and parsing text data. In this question, we are asked to construct a regular expression for the language of binary strings that do not begin with an "a".
Before we dive into constructing the regular expression, let's first clarify some basic concepts. In a binary alphabet, we have two symbols: 0 and 1. A binary string is a sequence of 0's and 1's. The length of a binary string is the number of symbols in the string. For example, "11001" is a binary string of length 5. A language over a binary alphabet is a set of binary strings. For example, the language of all binary strings of length 3 is {000, 001, 010, 011, 100, 101, 110, 111}.
Now, let's focus on the language of binary strings that do not begin with an "a". To construct a regular expression for this language, we need to define a pattern that matches any binary string that does not start with "a". In a binary alphabet, "a" is not a valid symbol, so we need to find a way to express this concept using the symbols that we have. One way to do this is to say that any binary string that does not start with "a" must start with either "0" or "1". We can express this using the following regular expression:
(0|1)*
This regular expression matches any number (including zero) of "0"s or "1"s. However, this regular expression also matches binary strings that start with "a". To exclude those strings, we need to add a condition that ensures the first symbol is not "a". We can express this condition by requiring that the first symbol is "1". We can modify the previous regular expression to achieve this:
1(0|1)*
This regular expression matches any binary string that starts with "1" and is followed by any number (including zero) of "0"s or "1"s. Since "a" is not a valid symbol in a binary alphabet, this regular expression matches any binary string that does not begin with "a".
To break this regular expression down further, we can start by looking at the first symbol, which is "1". This symbol matches only itself. The parentheses around the (0|1)* portion of the regular expression indicate that the enclosed expression can be repeated any number of times (including zero). The (0|1)* portion matches any number of "0"s or "1"s after the first "1". Together, this regular expression matches any binary string that starts with "1" and is followed by any number (including zero) of "0"s or "1"s, which is the language of binary strings that do not begin with an "a".
In conclusion, the regular expression for the language of binary strings that do not begin with an "a" is:
1(0|1)*
This regular expression matches any binary string that starts with "1" and is followed by any number (including zero) of "0"s or "1"s. It excludes binary strings that start with "a", which is not a valid symbol in a binary alphabet.
Step by stepSolved in 4 steps
- Consider the following C++ code segment: int d = 20; int f(int b) { static int c = 0; c *= b; return c; } int main() { int a; cin >> a; cout << f(a) * d << endl; }For each variable a, b, c, d: identify all type bindings and storage bindings for each binding, determine when the binding occurs identify the scope and lifetimearrow_forwardConsider the following structure definition. Write a C/C++ function that takes an array of struct student with its size and applies a curve system like if the student scored below 50, 1dd 10 points, if it is above 50, add 2 points. The lowest possible mark is 0 and the highest possible mark is 10. struct student{ int ID; int score; void applycurve (struct student a[ ], int size)arrow_forwardIn C language. Please don't copy similar programs from, bartleby or chegg Define a structure type auto_t to represent an automobile. Include components for the make and model (strings), the odometer reading, the manufacture and purchase dates (use another user-defined type called date_t), and the gas tank (use a user-defined type tank_t with components for tank capacity and current fuel level, giving both in gallons). Write I/O functions scan_date, scan_tank, scan_auto, print_date, print_tank, and print_auto, and also write a driver function that repeatedly fills and displays an auto structure variable until input is -30. Note: Each record has a number (1, 2, 3 ...),once the program scans record number -30, it should terminate without processing it. SAMPLE RUN #4: ./Structures Interactive Session Show Invisibles Highlight: Enter record number:1 Enter Make:Mercury Enter Model:Sable Enter Odometer Reading:99842 Enter Month:1 Enter Day:18 Enter Year:2001 Enter Month:5 Enter Day:30…arrow_forward
- Write a regular expression to describe each of the following languages. Example: {w € (a, b)* : w has both aa and bb as substrings} Regular expression: (a U b)* aa (a U b)* bb (a U b)* U (a U b)* bb (a U b)* aa (a U b)*arrow_forwardPlease help c++languagearrow_forwardI need help creating this C++ parser program that follows these rules in the image below.arrow_forward
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education