Abstract. A method for synthesizing an FSM specified in the logical language L* is considered. The method is based on translating the specification into the less expressive language L and applying the available method for synthesizing an FSM from the specification in this language. The resulting FSM may contain extra states called fictitious that have to be deleted. A simple method for checking the states for fictitiousness is proposed.

Keywords: specification language L*, ∃-formula, left-infinite word, quantifier elimination, synthesis of a finite-state machine, fictitious state.