introduction to finite automata

A finite-state automaton (FSA)
is a machine which takes, as input, a finite string of symbols from some alphabet ?. There is a finite set of states in which the machine can find itself. The state it is in before consuming any input is called the start state. Some of the states are accepting or final. If the machine ends in such a state after completely consuming an input string, the string is said to be accepted by the machine. The actual functioning of the machine is described by something called a transition function, which specifies what happens if the machine is in a particular state and looking at a particular input symbol.
The start state is labeling by "start" or minus sign"-"
The final state is labeling by "final " or plus sign"+"


Sometimes a start state is indicated by an arrow and a final state by drawing a box or another circle around its circle.

Transition table: is a table representation of a function ? that take two arguments and return a value. The rows of the table is the states and the columns is the input. The entry for the row with the state q and column for input a is the state ?(q,a).

1.1 Deterministic Finite Automata:
A deterministic finite automaton (DFA)—also known as deterministic finite state machine—is a finite state machine that accepts/rejects finite strings of symbols and only produces a unique computation (or run) of the automaton for each input string. A Deterministic Finite Automaton (DFA) consists of:
1. A finite set of states (Q, typically).
2. An input alphabet (?, typically).
3. A transition function (?, typically).
4. A start state (q0, in Q, typically).
5. A set of final states (F ? Q, typically).