Details
A deterministic finite automaton or DFA is a
finite-state machine that moves between states as it reads characters
from a string.
Each input consists of a table describing the DFA, and a quoted input
string, like so:
a b c d e f
> 0 0 0 0 1 0 0
1 0 0 0 1 0 2
2 3 0 0 1 0 0
F3 3 3 3 3 3 3
"adbacadafad"
In this table, we can find the following information:
-
There are four states, called
0
, 1
,
2
, and 3
.
- States are always digits
0-9
. There may be up to 10
states.
-
There are six characters in the input alphabet:
a
,
b
, c
, d
, e
, and
f
.
- Input characters may be lowercase letters
a-z
or digits
0-9
.
-
The table entries describe the new state for each (current state,
character) pair.
- For example, if the current state is
0
, and a
d
is read, the next state is 1
.
-
The row describing state
0
is marked with
>
so it is the initial state. There is
exactly one initial state.
-
The row describing state
3
is marked with
F
so it is an accept state. There may be
multiple accept states, or none at all.
Use the table to move the DFA between its states by feeding it
characters from the input string.
In our example:
- The initial state is
0
. The first character is
a
. Looking at the table, we see the new state is
0
.
- The current state is
0
. The next character is
d
. Looking at the table, we see the new state is
1
.
- The current state is
1
. The next character is
b
. Looking at the table, we see the new state is
0
.
- …
Finally, print the name of the state, followed by a space, followed
by either Accept
(if it is an accept state) or
Reject
(otherwise). In this case, we end in state
1
so we print 1 Reject
.
External links:
Wikipedia
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