A parenthesis string is a string of left and right parentheses. The string is well-formed 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.
Architectural Optimization for a 1.82Gbits/sec VLSI Implementation of the AES Rijndael Algorithm
