Applications like Yahoo, Facebook, Twitter have huge data which has to be stored and retrieved as per client access. This huge data storage requires huge database leading to increase in physical storage and becomes complex for analysis required in business growth. This storage capacity can be reduced and distributed processing of huge data can be done using Apache Hadoop which uses Map-reduce a...

Document listing is the problem of preprocessing a set of sequences, called documents, so that later, given a short string called the pattern, we retrieve the documents where the pattern appears. While optimal-time and linear-space solutions exist, the current emphasis is in reducing the space requirements. Current document listing solutions build on compressed suffix arrays. This paper is the ...

We describe a novel text compressor which combines Ziv-Lempel compression and arithmetic coding with a form of vector quantisation. The resulting compressor resembles an LZ-77 compressor, but with no explicit phrase lengths or coding for literals. An examination of the limitations on its performance leads to some predictions of the limits of LZ-77 compression in general, showing that the LZ-77 ...

One of the most famous and investigated lossless data-compression scheme is the one introduced by Lempel and Ziv about 40 years ago [23]. This compression scheme is known as ”dictionary-based compression” and consists of squeezing an input string by replacing some of its substrings with (shorter) codewords which are actually pointers to a dictionary of phrases built as the string is processed. ...

We consider the problem of decompressing the Lempel-Ziv 77 representation of a string S ∈ [σ] using a working space as close as possible to the size z of the input. The folklore solution for the problem runs in optimal O(n) time but requires random access to the whole decompressed text. A better solution is to convert LZ77 into a grammar of size O(z log(n/z)) and then stream S in optimal linear...

in this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in f(t,x(t))dt +g(t,x(t))dw_t$ in which the multifunction $f$ is semimonotone and hemicontinuous and the operator-valued multifunction $g$ satisfies a lipschitz condition. we define the it^{o} stochastic integral of operator set-valued stochastic pr...

Closed classes of three-valued logic generated by periodic symmetric funtions that equal 1 in tuples from {1, 2} and equal 0 on the rest tuples are considered. Criteria for bases existence and finite bases existence for these classes is obtained. The problem of the bases existence for some families of closed classes of the three-valued logic functions is considered in the paper. E. Post [1] (se...

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into equivalent sets of formulas in Kleene logic. For proof sea...

Łukasiewicz three-valued logic Ł3 is often understood as the set of 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using D...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...