UNIT I FINITE AUTOMATA
UNIT-I SYLLABUS • FINITE AUTOMATA : The Equivalence of Deterministic and Non-deterministic Finite Automata, Definition and Description of a Finite Automaton, Deterministic and Non- deterministic Finite State Machines, Acceptability of a String by a Finite Automaton, Mealy and Moore Machines, Minimization of Finite Automata, Basics of Strings and Alphabets, Transition Graph and Properties of Transition Functions, Regular Languages
Finite Automata • Finite automata are used to recognize patterns . • It takes the string of symbol as input and changes its state accordingly. When the desired symbol is found, then the transition occurs. • At the time of transition, the automata can either move to the next state or stay in the same state. • Finite automata have two states, Accept state or Reject state . When the input string is processed successfully, and the automata reached its final state, then it will accept.
Formal Definition of FA •A finite automaton is a collection of 5-tuple (Q, ∑, δ, q0, F), where:•Q: finite set of states •∑: finite set of the input symbol •q0: initial state •F: finalstate •δ: Transition function
Types of Automata • There are two types of finite automata: 1. DFA(deterministic finite automata) 2. NFA(non-deterministic finite automata)
Deterministic Finite Automata(DFA) • The finite automata are called deterministic finite automata if the m/c is read an i/p string one symbol at a time. • Deterministic refers to the uniqueness of the computation. • In the DFA, there is only one path for specific i/p from the current state to the next state. • DFA does not accept the null move i.e. DFA cannot change state without any i/p character.
• DFA can contain multiple final states . • It is used in lexical Analysis in compiler.
Formal Definition of DFA • A DFA can be represented by a 5-tuple (Q, ∑, δ, q 0 , F) where − • Q is a finite set of states. • ∑ is a finite set of symbols called the alphabet. • δ is the transition function where δ: Q × ∑ → Q • q 0 is the initial state from where any input is processed (q 0 Q). ∈ • F is a set of final state/states of Q (F Q). ⊆
Graphical Representation of a DFA
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- Spring '18
- isha mam
- Nondeterministic finite state machine, Automata theory, repeat step