Year: 2014
Type: dissertation
Abstract: Keeping in mind, that any context free language can be mapped to a subset of Dyck languages and by seeing various \ndatabase applications of Dyck, mainly verifying the well-formedness of XML file, we study the randomized streaming \nalgorithms for the recognition of Dyck(s) languages, with s different types of parenthesis. The main motivation of this \nwork is well known space bound for any T-pass streaming algorithm is \n(√n/T). \nLet x be the input stream of length n with maximum height hmax. Here we present a single-pass randomized streaming \nalgorithms to decide the membership of x in Dyck(s) using Counting Bloomfilter (CBF) with space O (hmax) bits, \nploylog(n) time per letter with two-sided error probability. Two-sided error is because of the false negative and false \npositives of counting bloomfilter. This algorithms denies the necessity of streaming reduction of Dyck(s) into Dyck(2), \nthat reduces the space even further by the factor of O (log s), compared to those uses streaming reduction. \nWe also present an improved single-pass randomized streaming algorithm for recognizing Dyck(2) with space O (√n) \nbits, which is the proven lower bound. Time bound is same polylog(n), as other existing algorithms and error is one-sided. \nIn this algorithm, we extended the existing approach of periodically compressing stack information. Existing approach \nuses two stacks and a linear hash function, instead of this we are using three stacks and same linear hash function to \nachieve space lower bound of O (√n). \nWe also present another single-pass streaming algorithm with O (hmax) space that uses counting bloomfilter and \ndirectly acts on Dyck(s)
Author: Akash Jain
Language: English
Subfield: Theoretical Computer Science
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2274205071