In 29—47, design a finite-state automaton to accept the language defined by the regular expression in the referenced exercise from Section 12.1.

46. Exercise 38

Design a finite-state automaton to accept the language defined by the regular expression for all telephone numbers that have three digits, then a hyphen, then three more digits, then a hyphen, and then four digits, where the first three digits are either 800 or 888 and the last four digits start and end with a 2.

Given information:

All telephone numbers that have three digits, then a hyphen,then three more digits, then a hyphen, and then four digits,where the first three digits are either 800 or 888 and the lastfour digits start and end with a 2.

Calculation:

Given:

All telephone numbers where the first three digits are 800 or 888 and the last four digits starts with a 2 and end with a 2.

A telephone number contains 3 digits, followed by a hyphen-, followed by 3 digits, followed by a hyphen- and ending with 4 digits.

Let [0−9] represent all digits 0,1,2,3,4,6,7,8,9.

Let us design an automaton with 14 states s0,s1,...,s13 where s0 is the initial state. We draw each of the state as a circle with the name of the state within the circle. We draw an arrow towards the initial state and draw a second circle within the accepting states.

s0=Initial states1= Input is 8s2= Input is 80

s3= input is 88

s4= Input is 800 or 888s5= input starts with 800 or 888, followed by a hyphen

s6=Input starts with 800 or 888, followed by a hyphen, followed by a digit

s7= Input starts with 800 or 888, followed by a hyphen, followed by 2 digits

s8= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits

s9= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits, followed by a hyphen

s10= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits,         followed by a hyphen, followed by a 2

s11= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits,         followed by a hyphen, followed by a 2, followed by one digit

s12= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits,         followed by a hyphen, followed by a 2, followed by two digits

s13= Input starts with 800 or 888, followed by a hyphen, followed by 3 digits,         followed by a hyphen, followed by a 2, followed by two digits, followed by a 2

s14=Remaining inputs

We then note that the state s₁₃ corresponds with inputs that are telephone numbers where the first three digits are 800 or 888 and where the final four digits start with a 2 and end with a 2, thus s₁₁ is the accepting state