CPSC $323$ Homework One

Below you will find a diagram of a deterministic finite automaton. As warm$-$up for

problem two, please:

a$.$ List the following:

i$.$ The set of states, $Q$

ii$.$ The set of characters $($the alphabet$),$

iii. The transition function, $$:$QQ$

iv$.$ The start state, $q_0$

v$.$ The set of accept states, FsubeQ

b$.$ Describe the language that this DFA recognizes.

Recall the in$-$class exercise from Thursday, $08\mathrm{.}29\mathrm{.}24,$ where you were asked to create a

deterministic finite automaton that recognized integers. Using that as a reference, design

a DFA that recognizes decimal numbers, often called floats in programming languages.

a$.$ Some things to keep in mind:

i$.$ A decimal number can start with a zero.

ii$.$ A decimal number can be positive or it can be negative or zero.

iii. A decimal number can be infinite in length, much like an integer.

iv$.$ Your machine should not allow for more than one decimal or negative

symbol to appear for a given. That is$,$ if your machine allows transitions

back to earlier states, it should not allow another decimal point or another

negative sign to appear in the number.

b$.$ To receive full credit for this problem, you must:

i$.$ Design a machine that correctly recognizes decimal numbers.

ii$.$ Utilize the formal definition of a DFA, specifying:

The set of states, $Q$

The set of characters $($the alphabet$),$

The transition function, $$:$QQ$

The start state, $q_0$

The set of accept states, FsubeQ

iii. Provide a diagram of your DFA.