JNTU B.Tech II FORMAL LANGUAGES AND AUTOMATA THEORY Previous Question Paper (September/October - 2023 - R15)

A string is accepted by a finite automaton if, starting from the initial state, the sequence of transitions triggered by the input symbols leads the automaton to reach one of its designated final states (or accepting states) after processing the entire string. If the automaton ends in a non-accepting state, the string is rejected.

An NFA with ε-transitions (NFA-ε) is a non-deterministic finite automaton that allows transitions between states without consuming any input symbol. These transitions, denoted by the Greek letter ε, allow the automaton to change its state spontaneously. This feature simplifies the design of complex automata by allowing the concatenation of smaller machines.

Formally, an NFA-ε is defined as a 5-tuple (Q, Σ, δ, q₀, F), where the transition function δ is defined as δ: Q × (Σ ∪ {ε}) → 2^Q. The inclusion of ε in the domain allows for transitions that do not require an input character.

For example, consider an NFA-ε that accepts strings starting with 'a' or 'b' followed by 'c'. We can have a start state q₀ with ε-transitions to state q₁ (processing 'a') and state q₂ (processing 'b'). From both q₁ and q₂, there is a transition on 'c' to a final state q₃. This structure allows the machine to non-deterministically choose between paths without reading any input at the start.