Dead State in DFA


In automata theory, a Dead State (also known as a trap state or rejecting state) is a key concept in the design and analysis of deterministic finite automata.

What is a Dead State?

A dead state is a state in a DFA from which no sequence of inputs can lead to an accepting (final) state.Once the automaton enters a dead state, it cannot recover or proceed to an accepting state regardless of the inputs that follow.

Key Characteristics:
A dead state is never an accepting or final state in the automaton.
Once entered, all transitions from a dead state lead either back to itself or to other dead states.
It typically represents a condition where the input string can no longer be accepted, indicating failure or invalid input.

Why Do We Use Dead States?

Dead states help:
  • Complete the transition function (especially in total DFAs).
  • Represent invalid or non-accepted paths explicitly.
  • Assist in error detection and rejection in language recognition.
Dead State Example
Consider a DFA that accepts only the binary string “10”.Dead State Example in DFA

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