Abstract
We present two EREW PRAM algorithms and one CREW PRAM algorithm for solving set recurrence equations of the type commonly used in dynamic programming solutions to many problems in pattern matching, sequence comparison, and language recognition. All three algorithms run in O(log 2 n) time. The first EREW PRAM algorithm uses O( M( n/log n)log 2 n) processors, where M( n) is the number of processors needed to multiply two n × n Boolean matrices in O(log n) time on an EREW PRAM. The second EREW PRAM algorithm uses O( M′( n/(log n[formula]))log 2 n) processors, where M′( n) is the number of processors needed to multiply two n × n matrices over an arbitrary ring in O(log n) time on an EREW PRAM. The CREW PRAM algorithm uses O(M″(n/log 1.5n )log 2n) processors, where M″( n) is the number of processors needed to multiply two n × n matrices over an arbitrary ring in O(log n) time on a CREW PRAM. As an application, we show that linear context-free languages can be recognized in O(log 2 n) time using o( M( n)) processors on an EREW PRAM. This result answers an open question in Atallah et al. (in "Proceedings, ACM Symp. on Parallel Alg. and Arch. 1989," pp. 421-431).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.