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 / b / i / Solution

Every finite formal language is a regular language. A single string $a_1\cdots a_k$ is described by the regular expression formed by concatenating its symbols; the empty string is described by $\epsilon$. A finite union of these regular expressions describes any specified finite collection of strings. The empty collection is described by $\varnothing$. ThusEquivalently, a deterministic finite automaton can remember which prefix of one of the finitely many accepted strings has been read, moving to a rejecting dead state when no such prefix remains possible.