Section: New Results

A probabilistic Kleene theorem

In [63] , we establish a Kleene theorem for (Rabin) probabilistic automata over finite words. Probabilistic automata generalize deterministic finite automata and assign to a word an acceptance probability. For convenient specification of probabilistic queries, we provide probabilistic expressions with probabilistic choice, guarded choice, concatenation, and a star operator. Our expressions are closer to language-theoretic operations than previous calculi for probabilistic systems, which were rather motivated by system modeling than query answering. We prove that probabilistic expressions and probabilistic automata are expressively equivalent. Our result extends to two-way probabilistic automata with pebbles and corresponding expressions.