In this work, we ask you to design a deterministic Finite Automaton (FA) to recognise arithmetic expressions. When we say arithmetic expression, we mean a kind of expression you can type in a very basic desk calculator. That is, neither variables nor brackets are allowed. It contains only numbers and four arithmetic operators, +, -, *, and /. The following are some examples of arithmetic expression: 1. Any number string with or without signs - e.g. 3, -1, +10, 3.14, -0.70 and 099. 2. Number strings mixed with arithmetic operators e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2. An example of FA diagram for recognising a non- negative integer is given below. You may use it as a start point. You need to add a few more states and transitions to handle numbers with decimal point and signs (e.g. -5, +2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most importantly, you also need to add a few more things to deal with the arithmetic operators +, -, *, /. start 0-9 digit 0-9
In this work, we ask you to design a deterministic Finite Automaton (FA) to recognise arithmetic expressions. When we say arithmetic expression, we mean a kind of expression you can type in a very basic desk calculator. That is, neither variables nor brackets are allowed. It contains only numbers and four arithmetic operators, +, -, *, and /. The following are some examples of arithmetic expression: 1. Any number string with or without signs - e.g. 3, -1, +10, 3.14, -0.70 and 099. 2. Number strings mixed with arithmetic operators e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2. An example of FA diagram for recognising a non- negative integer is given below. You may use it as a start point. You need to add a few more states and transitions to handle numbers with decimal point and signs (e.g. -5, +2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most importantly, you also need to add a few more things to deal with the arithmetic operators +, -, *, /. start 0-9 digit 0-9
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
Problem 1PE
Related questions
Question
![In this work, we ask you to design a deterministic
Finite Automaton (FA) to recognise arithmetic
expressions.
When we say arithmetic expression, we mean a kind of
expression you can type in a very basic desk calculator.
That is, neither variables nor brackets are allowed. It
contains only numbers and four arithmetic operators, +,
-, *, and /.
The following are some examples of arithmetic
expression:
1. Any number string with or without signs - e.g. 3, -1,
+10, 3.14, -0.70 and 099.
2. Number strings mixed with arithmetic operators
e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2.
An example of FA diagram for recognising a non-
negative integer is given below. You may use it as a start
point. You need to add a few more states and transitions
to handle numbers with decimal point and signs (e.g. -5,
+2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most
importantly, you also need to add a few more things to
deal with the arithmetic operators +, -, *, /.
→start
0-9
digit 0-9](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0afc403-0a89-46bc-8d2d-224fd73b8b73%2Fd8178c2e-76e9-4089-9165-dec48bb41ca2%2Fi9bsqlb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this work, we ask you to design a deterministic
Finite Automaton (FA) to recognise arithmetic
expressions.
When we say arithmetic expression, we mean a kind of
expression you can type in a very basic desk calculator.
That is, neither variables nor brackets are allowed. It
contains only numbers and four arithmetic operators, +,
-, *, and /.
The following are some examples of arithmetic
expression:
1. Any number string with or without signs - e.g. 3, -1,
+10, 3.14, -0.70 and 099.
2. Number strings mixed with arithmetic operators
e.g. 3+5, -1+2*3, 7/10-0.7, and -1.4-+8.2.
An example of FA diagram for recognising a non-
negative integer is given below. You may use it as a start
point. You need to add a few more states and transitions
to handle numbers with decimal point and signs (e.g. -5,
+2, 0.21, -32.6, +99.05, but not the form 1.0E-3). Most
importantly, you also need to add a few more things to
deal with the arithmetic operators +, -, *, /.
→start
0-9
digit 0-9
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