A note on log space optimization

Abstract

We show that computing iterated multiplication of word matrices over {0,1}, using the operations maximum and concatenation, is complete for the class optL of log space optimization functions. The same problem for word matrices over {1} is complete for the class FNL of nondeterministic log space functions. Improving previously obtained results, we furthermore place the class optL in AC, and characterize FNL by restricted log space optimization functions.