Designing a Systolic Algorithm for Generating Well-Formed Parenthesis Strings

Abstract

A parenthesis string is a string of left and right parentheses. The string is wellformed when it consists of balanced pairs of left and right parentheses. This study presents a novel systolic algorithm for generating all the well-formed parenthesis strings in lexicographical order. The algorithm is cost-optimal and is run on a linear array of processors such that each well-formed parenthesis string can be generated in three time steps. The processor array is appropriate for VLSI implementation, since it has the features of modularity, regularity, and local connection.

Alpha-Numeric Notation for one Data Structure in Software Engineering

“…The tree is represented by a string P of balanced parentheses of length 2n. A node is represented by a pair of matching parentheses "()" and all sub-trees rooted at the node are encoded in an order between the matching parentheses [2,13].…”