Nondeterministic Finite Automaton (NFA) and Deterministic Finite Automaton (DFA) are two types of finite state machines used in computer science and theoretical computer science. Here are five key differences between NFA and DFA:
Transition Function:
NFA: In an NFA, a state may have multiple transitions on the same input symbol, and it may also have ε (epsilon) transitions, where the machine can move to the next state without consuming any input.
DFA: In a DFA, each state has a unique transition for every input symbol in the alphabet. There are no ε transitions, and the machine always transitions to a single next state on any given input.
Acceptance Criteria:
NFA: An NFA accepts a string if there exists at least one possible path (sequence of transitions) that leads to an accepting state. Non-determinism allows multiple choices at each step.
DFA: A DFA accepts a string only if there is a unique path (sequence of transitions) from the start state to an accepting state for the entire input string. Determinism ensures a single, unambiguous computation path.
Representation of Rejected Inputs:
NFA: An NFA rejects an input if all possible paths result in a non-accepting state. Rejection occurs when there is no valid computation path.
DFA: A DFA rejects an input as soon as it encounters a non-accepting state during the computation. There is no backtracking or exploration of alternative paths.
Transition Table:
NFA: The transition table of an NFA may have multiple entries for a single state and input symbol, representing the multiple possible transitions.
DFA: The transition table of a DFA has a single entry for each state and input symbol, indicating the unique next state for each combination.
Memory Requirements:
NFA: Nondeterministic machines generally require less memory because they do not need to remember the exact path taken during computation. They explore possibilities simultaneously.
DFA: Deterministic machines may require more memory since they need to remember the entire computation path to make decisions. Each state transition is explicitly defined.
In summary, the main distinction between NFAs and DFAs lies in their approach to handling multiple transitions and choices during computation. NFAs allow non-determinism and multiple transitions, while DFAs enforce determinism with a single, unique transition for each state and input symbol combination. Both NFAs and DFAs are fundamental concepts in automata theory and play important roles in the study of formal languages and computational models.