p$2$ CS $314$ Spring $2018$ Final Exam Name $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

I. Suppose $$unsigned real numbers$$ in some language must have exactly one decimal

point, and the decimal point must be immediately preceded and followed by one or

more digits. E$.$g$.,\mathrm{.}7$ and $5.$ are not legal unsigned real numbers, nor is $3$ but $0\mathrm{.}1$ is$.$

Write a regular expression for these unsigned real numbers. You may use the letter

d to stand for the digits $0$ through $9.$

II$.$ Consider the following Finite State Automaton $($FSA$)$

A$.$ Is this a deterministic or a non$-$deterministic FSA? Why?

B$.$ Write a regular expression that specifies the same language that this FSA

accepts.

C$.$ For each of the following strings, if it is accepted by the FSA above circle Yes

and give a sequence of states that proves it is accepted. If not, circle No$.$

i$.$ a Yes: states $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ No

ii$.$ a b c Yes: states $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ No

iii. a b a c Yes: states $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ No

iv$.$ a b b c Yes: states $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ No

v$.$ a b a b a b c Yes: states $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$ No