One of the most intricate algorithms related to words is Makanin's algorithm solving word equations. The algorithm is very complicated and the complexity of the problem of solving word equations is not well understood. Word equations can be used to deene various properties of strings, e.g. general versions of pattern-matching with variables. This paper is devoted to introduce a new approach and...

Lempel and Ziv (1976) proposed a computable string production-complexity. In this paper, our emphasis is on providing the rigorous development, where possible, for the theoretical aspects of a more recent and contrasting measure of string complexity. We derive expressions for complexity bounds subject to certain constraints. We derive an analytic approximation to the upper bound to linearize th...

It is known that elementary cellular automaton rule 110 is capable of supporting universal computation by emulating cyclic tag system. Since the whole information necessary to perform computation is stored in the configuration, it is reasonable to investigate the complexity of configuration for the analysis of computing process. In this research we employed Lempel-Ziv complexity as a measure of...

Wyner-Ziv (WZ) encoder is a low -complexity encoder and can be made to achieve compression comparable to traditional high complexity encoders but at the expense of a high-complexity decoder. The high complexity of the decoder is mainly attributed to the generation of side information which involves motion estimation. In this paper sub-pixel motion estimation and intra-prediction based on H.264 ...

The complexity of computing the Lempel-Ziv factorization and the set of all runs (= maximal repetitions) is studied in the decision tree model of computation over ordered alphabet. It is known that both these problems can be solved by RAM algorithms in O(n log σ) time, where n is the length of the input string and σ is the number of distinct letters in it. We prove an Ω(n log σ) lower bound on ...

De Agostino, S., P-complete problems in data compression, Theoretical Computer Science 127 (1994) 181-186. In this paper we study the parallel computational complexity of some methods for compressing data via textual substitution. We show that the Ziv-Lempel algorithm and two standard variations are P-complete. Hence an efficient parallelization of these algorithms is not possible uqless P = NC.