The universality and linearity of compression by substring enumeration

A new lossless data compression technique called compression by substring enumeration (CSE) has recently been introduced. Two conjectures have been stated in the original paper and they have not been proved there nor in subsequent papers on CSE. The first conjecture says that CSE is universal for Markovian sources, provided an appropriate predictor is devised. The second one says that CSE has a linear complexity both in time and in space. In this paper, we present an appropriate predictor and demonstrate that CSE indeed becomes universal for any order-k Markovian source. Finally, we prove that the compacted substring tree on which CSE´s linear complexity depends effectively has linear size.