Abstract
Given a class Open image in new window of languages, let Pol( Open image in new window ) be the polynomial closure of Open image in new window , that is, the smallest class of languages containing Open image in new window and closed under the operations union and marked product L a L', where a is a letter. We determine the polynomial closure of various classes of rational languages and we study the properties of polynomial closures. For instance, if Open image in new window is closed under quotients (resp. quotients and inverse morphism) then Pol( Open image in new window ) has the same property. Our main result shows that if Open image in new window is a boolean algebra closed under quotients then Pol( Open image in new window ) is closed under intersection. As an application, we refine the concatenation hierarchy introduced by Straubing and we show that the levels 1/2 and 3/2 of this hierarchy are decidable.
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.
