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\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}} \newcommand{\betaReduction}[0] {\rightarrow_{\beta}} \newcommand{\betaEq}[0] {=_{\beta}} \newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}} \newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}} \)
Math and science::Theory of Computation

Alphabets and languages

An alphabet is defined to be any [...]. The members of an alphabet are [...] of the alphabet.

A [something over something] is a finite sequence of symbols from that alphabet.

A language is [...]. A language is [...] if no member is a proper prefix of another.

A string is a proper prefix of another if it is a prefix but not equal to the other.

We say that a finite machine \( M \) [...] if \( A = \{w | M \text{ accepts } w \} \). A language is called a [...] if some finite automaton recognizes it.