Abstract
The first step when forming the polynomial hierarchies of languages is to consider languages of the form KaL where K and L are over a finite alphabet A and from a given variety V of languages, a being a letter from A. All such KaL's generate the variety of languages BPol1(V). We estimate the numerical parameters of the language KaL in terms of their values for K and L. These parameters include the state complexity of the minimal complete DFA and the size of the syntactic monoids. We also estimate the cardinality of the image of A* in the Schuetzenberger product of the syntactic monoids of K and L. In these three cases we obtain the optimal bounds. Finally, we also consider estimates for the cardinalities of free monoids in the variety of monoids corresponding to BPol1(V) in terms of sizes of the free monoids in the variety of monoids corresponding to V.
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 callMore From: Electronic Proceedings in Theoretical Computer Science
Disclaimer: 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.
