Beth's theorem

Beth's theorem is a key result in automata theory and logic that links the behavior of abstract machines, called automata, with formal logical systems. It states that for certain well-defined automata and logical structures, the set of problems the automaton can recognize exactly matches the set of properties expressible within a specific logical language. Essentially, it provides a correspondence between computational capability and logical expressibility, helping us understand which problems can be decided or recognized by machines and how these problems relate to logical descriptions.