K-lossless sequential machines of maximum order

Abstract

A finite state sequential machine is said to be k-lossless, or information lossless of order k, if a knowledge of the initial state and first k output symbols is always sufficient to uniquely determine the first input symbol. For n-state sequential machines, the value of k is such that l ≤ k ≤½ n(n - l) + l e kmax. It has been shown that machines of order kmax can be constructed if the output alphabet contains 6 symbols.1 In this paper, it is shown that for binary output machines, the maximum value of k is strictly less than kmax.