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Communication Complexity And Linearly Ordered Sets

100%
Kula M., Serwecińska M.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
93-117
EN
The paper is devoted to the communication complexity of lattice operations in linearly ordered finite sets. All well known techniques ([4, Chapter 1]) to determine the communication complexity of the infimum function in linear lattices disappoint, because a gap between the lower and upper bound is equal to O(log2 n), where n is the cardinality of the lattice. Therefore our aim will be to investigate the communication complexity of the function more carefully. We consider a family of so called interval protocols and we construct the interval protocols for the infimum. We prove that the constructed protocols are optimal in the family of interval protocols. It is still open problem to compute the communication complexity of constructed protocols but the numerical experiments show that their complexity is less than the complexity of known protocols for the infimum function.
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Algebra of Polynomially Bounded Sequences and Negligible Functions

76%
Okazaki H.
Formalized Mathematics
|
2015
|
tom 23
|
nr 4
371-378
EN
In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially bounded sequences, using negligible functions.
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