DFA Definition

Learning Goal: I’m working on a bash question and need an explanation and answer to help me learn.DFA DefinitionThe DFA definition file has the format:

…Alphabet: This is simply the list of characters in the alphabet, without spaces. For example, if the alphabet is {0,1}” role=”presentation” style=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;” rel=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;”>{0,1}{0,1}, then the first line of the DFA definition is simply 01.Number of states and state identifiers: The number of states is simply an integer. So the second line would be 10 for a 10-state DFA. The states of an n” role=”presentation” style=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;” rel=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;”>nn-state DFA are numbered 0″ role=”presentation” style=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;” rel=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;”>00 through n−1″ role=”presentation” style=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;” rel=”display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; transition: none 0s ease 0s; position: relative; vertical-align: 0px; box-sizing: content-box;”>n−1n−1.Start state: This line contains a single number, the number of the start state.Accepting states: This is a list of state numbers, separated by spaces. For example, if the DFA has states 3, 5, and 7 as accepting states, this line is 3 5 7.Transitions for states: There are as many lines in the representation of the transition function as the DFA has states. The first line lists the transitions for state 0, the second line for state 1, and so on. Each line is a sequence of integers separated by spaces. The number of integers is exactly the same as the size of the alphabet. The first integer is the state the DFA transitions to from the current state if it reads the first character in the alphabet. The second integer is the state the DFA transitions to from the current state if it reads the second character in the alphabet. And so on.As an example, here is the file describing the DFA in the following figure:ab
2
0
1
0 1
1 0Inputs and OutputsThe input file contains a bunch of strings, one per line. For example,abbabaabba
ababbabbba
abcIf we were to run the above example DFA on this input file, the output file should have the following contents:ACCEPT
REJECT
INVALIDThis is because the first string has an odd number of bs, which is exactly the type of string this DFA accepts. The second string has an even number of bs. It is thus rejected by the DFA. The final string contains the character c, which is not part of the DFAs alphabet. So the DFA flags this input as INVALID.
Requirements: 3h   |   .doc file

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