Select Page

Deterministic Finite Automaton (DFA) and Nondeterministic Finite Automaton (NFA) are two types of abstract computational models used in automata theory and formal language theory to represent and analyze finite state machines. Here are their definitions:

  1. Deterministic Finite Automaton (DFA):
    • A DFA is a mathematical model consisting of a finite set of states, a finite alphabet of input symbols, a transition function that maps each state and input symbol pair to a unique next state, a designated start state, and a set of one or more designated accept states.
    • At each step, the DFA reads an input symbol and transitions from its current state to a new state based on the current state and the input symbol according to the transition function.
    • The DFA accepts a string if, after reading the entire string, it ends up in one of the accept states.
    • The key characteristic of a DFA is that for any given state and input symbol, there is only one possible next state.
  2. Nondeterministic Finite Automaton (NFA):
    • An NFA is similar to a DFA but differs in that it allows for multiple possible transitions from a given state with a given input symbol or the possibility of transitioning to multiple states without consuming any input symbol.
    • Formally, an NFA is defined as a 5-tuple (Q, Σ, δ, q0, F), where Q is a finite set of states, Σ is the input alphabet, δ is the transition function that maps each state and input symbol pair to a set of possible next states (which may be empty), q0 is the start state, and F is the set of accept states.
    • An NFA accepts a string if there exists at least one sequence of transitions (or path) that leads to an accept state when the entire string is read.
    • The nondeterminism in NFAs allows for simpler representations of certain languages compared to DFAs, but the trade-off is that algorithms for processing NFAs are often more complex.

DFAs and NFAs are both types of finite automata used to recognize languages, with DFAs having deterministic transitions and NFAs allowing for nondeterministic transitions.