Abstract

We prove that the ranking problem for unambiguous context-free languages is NC 1-reducible to the value problem for algebraic formal power series in noncommuting variables. In the particular case of regular languages we show that the problem of ranking is NC 1-reducible to the problem of counting the number of strings of given length in suitable regular languages. As a consequence ranking problems for regular languages are NC 1-reducible to integer division and hence computable by log-space uniform boolean circuits of polynomial size and depth O(log n log log n), or by P-uniform boolean circuits of polynomial size and depth O(log n).

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 call

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.