Past exam of the year 1 of the computer science course of the University of Oxford / 2005 / Calculus, linear algebra, discrete mathematics, logic and proof, and models of computation / 9 / a / Solution

A regular language over a finite alphabet is a formal language recognized by a deterministic finite automaton; equivalently it is described by a regular expression. A nondeterministic finite automaton accepts an input string if at least one permitted computation consumes that string and reaches an accepting state. The connection is the equivalenceEvery deterministic finite automaton is a special case of a nondeterministic finite automaton. Conversely, the subset construction makes a deterministic finite automaton whose states record the set of all possible current states of a nondeterministic finite automaton. After each input symbol, update that set by taking all permitted transitions, also including any epsilon closure. A new state is accepting exactly when it contains an old accepting state. A finite state set has finitely many subsets, so this really is a deterministic finite automaton recognizing the same formal language.