Abstract
Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set of input symbols giving rise to state transitions but rather as a set of output symbols generated during spontaneous state transitions; in addition, it is assumed that automata can be “controlled” through the imposition of certain allowable restrictions on the set of symbols that may be generated at a given instant. The problems in question are then recast as that of deciding membership in a deterministic Rabin automaton's controllability subset — the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The new formulation leads to a direct, efficient and natural solution based on a fixpoint representation of the controllability subset. This approach combines advantages of earlier solutions and admits useful extensions incorporating liveness assumptions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
