This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived. Moreover, since most graphs are prime although they can have a product-like structure, also known as approximate graph products, the practical application of the...

We construct a signature scheme that is proved secure, without random oracles, under the strong RSA assumption. Unlike other efficient strong-RSA based schemes, the new scheme does not generate large prime numbers during signing. The public key size and signature size are competitive with other strong RSA schemes, but verification is less efficient. The new scheme adapts the prefix signing tech...

The concept of quasi-ordered residuated system was introduced in 2018 by Bonzio and Chajda. author analyzed the filters as well some types such an algebraic system. Additionally, also dealt with a strong which he determined prime irreducible filters. In this paper, introduce three analyze their interconnections.

The practical application of graph prime factorization algorithms is limited in practice by unavoidable noise in the data. A first step towards error-tolerant “approximate” prime factorization, is the development of local approaches that cover the graph by factorizable patches and then use this information to derive global factors. We present here a local, quasi-linear algorithm for the prime f...

Consider a procedure that chooses fe-bit odd numbers independently and from the uniform distribution, subjects each number to t independent iterations of the strong probable prime test (Miller-Rabin test) with randomly chosen bases, and outputs the first number found that passes all t tests. Let pfc , denote the probability that this procedure returns a composite number. We obtain numerical upp...

Recently, Damg̊ard, Landrock and Pomerance described a procedure in which a k-bit odd number is chosen at random and subjected to t random strong probable prime tests. If the chosen number passes all t tests, then the procedure will return that number; otherwise, another k-bit odd integer is selected and then tested. The procedure ends when a number that passes all t tests is found. Let pk,t den...

we consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $x$, $(x, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $x$. we also show that, for a strong residuated lattice $x$, $bigcap {p_{lambda} ,|,p_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Let a measurement consist of a linear combination of damped complex exponential modes, plus noise. The problem is to estimate the parameters of these modes, as in line spectrum estimation, vibration analysis, speech processing, system identification, and direction of arrival estimation. Our results differ from standard results of modal analysis to the extent that we consider sparse and co-prime...