Sublinear Parallel Time Recognition of Tree Adjoining Languages

A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in computational Linguistics. This class of languages is known to properly include all context-free languages; for example, the non-context-free sets {anbncn} and {ww) are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrentread, exclusive-write parallel random-access machine (CREW PRAM) in 0 (log2(n)) time using polynomially many processors. This extends a previous result for context-free languages. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-66. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/689 SUBLINEAR PARALLEL TIME RECOGNITION OF TREE ADJOINING LANGUAGES Michael A. Palis and Sunll Shende MS-CIS-88-66 LlNC LAB 127 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 191 04 August 1988 Acknowledgements: This research was supported in part by DARPA grant N00014-85K-0018, NSF grants MCS-82-07294, DCR-84-10413, MCS-83-05221, MCS-8219196-CER, IR184-10413-A02 and U.S. Army grants DAA29-84-K-0061, DAA29-84-9-0027. Sublinear Parallel Time Recognition of Tree Adjoining ~anguages* Michael A. Palis and Sunil Shende Department of Computer and Information Science University of Pennsylvania Philadelphia, PA 19 104-6389 Abstract A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in computational Linguistics. This class of languages is known to properly include all context-free languages; for example, the non-context-free sets {a" bncn} and { w w ) are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent-read, exclusive-write parallel random-access machine (CREW PRAM) in 0 (log2(n)) time using polynomially many processors. This extends a previous result for context-free languages.A parallel algorithm is presented for recognizing the class of languages generated by tree adjoining grammars, a tree rewriting system which has applications in computational Linguistics. This class of languages is known to properly include all context-free languages; for example, the non-context-free sets {a" bncn} and { w w ) are in this class. It is shown that the recognition problem for tree adjoining languages can be solved by a concurrent-read, exclusive-write parallel random-access machine (CREW PRAM) in 0 (log2(n)) time using polynomially many processors. This extends a previous result for context-free languages. * Research supported in part by ARO grant DA.429-84-9-0027, NSF grants MCS-8219116-CER, MCS-82-07294, DCR-84-104 13, MCS-83-05221, and DARPA grant N00014-85-K-0018.