1 research outputs found
Randomness of formal languages via automatic martingales
We define a notion of randomness for individual and collections of formal
languages based on automatic martingales acting on sequences of words from some
underlying domain. An automatic martingale bets if the incoming word belongs to
the target language or not. Then randomness of both single languages and
collections of languages is defined as a failure of automatic martingale to
gain an unbounded capital by betting on the target language according to an
incoming sequence of words, or a text. The randomness of formal languages
turned out to be heavily dependent on the text. For very general classes of
texts, any nonregular language happens to be random when considered
individually. As for collections of languages, very general classes of texts
permits nonrandomness of automatic families of languages only. On the other
hand, an arbitrary computable language is be shown to be nonrandom under
certain dynamic texts