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 ...

The aim of this note is to provide some reference facts for LZW---mostly from Thomas and Cover \cite{Cover:2006aa} and provide a reference for some metrics that can be derived from it. LZW is an algorithm to compute a Kolmogorov Complexity estimate derived from a limited programming language that only allows copy and insertion in strings (not Turing complete set). Despite its delightful simplic...

We explore the use of the LZW and LZSS data compression methods. These methods or some versions of them are very common in use of compressing different types of data. Even though on average LZSS gives better compression results, we determine the case in which the LZW perform best and when the compression efficiency gap between the LZW algorithm and its LZSS counterpart is the largest.

The goal of this research is twofold: (i) to analyze generalized digital search trees, and (ii) to derive the average proole (i.e., phrase length) of a generalization of the well known parsing algorithm due to Lempel and Ziv. In the generalized Lempel-Ziv parsing scheme, one partitions a sequence of symbols from a nite alphabet into phrases such that the new phrase is the longest substring seen...

The Lempel-Ziv parsing (LZ77) is a widely popular construction lying at the heart of many compression algorithms. These algorithms usually treat data as sequence bytes, i.e., blocks fixed length 8. Another common option to view bits. We investigate following natural question: what relationship between LZ77 parsings same interpreted fixed-length and bits (or other “elementary” letters)? In this ...

By interpreting ‘p is impossible’ by ‘p is selfcontradictory’, and ‘p is always’ by ‘not p is self-contradictory’, this paper studies which of the three-valued systems of Łucasiewicz, Gödel, Kleene, Bochvar, and Post, do verify the Aristotle’s principles of Non-Contradiction (NC), and Excluded-Middle (EM). Keywords— Systems of three-valued logic, Non-Contradiction, Excluded-Middle.