scholarly journals Random Integer Lattice Generation via the Hermite Normal Form

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1509
Author(s):  
Gengran Hu ◽  
Lin You ◽  
Liang Li ◽  
Liqin Hu ◽  
Hui Wang
Keyword(s):  
Normal Form ◽  
Integer Lattice ◽  
Random Input ◽  
Generation Algorithm ◽  
Integer Lattices ◽  
Hermite Normal Form ◽  
Random Integer ◽  
Lattice Algorithms ◽  
Definition Of

Lattices used in cryptography are integer lattices. Defining and generating a “random integer lattice” are interesting topics. A generation algorithm for a random integer lattice can be used to serve as a random input of all the lattice algorithms. In this paper, we recall the definition of the random integer lattice given by G. Hu et al. and present an improved generation algorithm for it via the Hermite normal form. It can be proven that with probability ≥0.99, this algorithm outputs an n-dim random integer lattice within O(n2) operations.

scholarly journals A Note on Decomposable and Reducible Integer Matrices

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1125
Author(s):  
Carlos Marijuán ◽  
Ignacio Ojeda ◽  
Alberto Vigneron-Tenorio
Keyword(s):  
Normal Form ◽  
Linear Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Integer Matrix ◽  
Hermite Normal Form ◽  
Necessary And Sufficient

We propose necessary and sufficient conditions for an integer matrix to be decomposable in terms of its Hermite normal form. Specifically, to each integer matrix, we associate a symmetric integer matrix whose reducibility can be efficiently determined by elementary linear algebra techniques, and which completely determines the decomposability of the first one.

Hermite Normal Form Computation Using Modulo Determinant Arithmetic

1987 ◽  
Vol 12 (1) ◽  
pp. 50-59 ◽  
Author(s):  
P. D. Domich ◽  
R. Kannan ◽  
L. E. Trotter
Keyword(s):  
Normal Form ◽  
Hermite Normal Form

Random size trees on the one and two dimensional integer lattice

1969 ◽  
Vol 6 (02) ◽  
pp. 301-308
Author(s):  
A.M.V. Verhagen
Keyword(s):  
Stochastic Process ◽  
Continuous Distribution ◽  
Integer Lattice ◽  
Two Dimensional ◽  
Random Size ◽  
Integer Lattices ◽  
The One

A stochastic process in which any tree in a forest planted on an integer lattice eliminates its four neighbours when it exceeds their heights, is studied for the case when all heights are independent samples from a continuous distribution. The proportion of the trees of the forest eliminated in this manner is determined for both the one and the two dimensional integer lattices.

Storage efficient algorithm for Hermite Normal Form using LLL

2021 ◽  
Vol 613 ◽  
pp. 183-200
Author(s):  
Gook Hwa Cho ◽  
Hyang-Sook Lee ◽  
Seongan Lim ◽  
Yoonjeong Kim
Keyword(s):  
Normal Form ◽  
Efficient Algorithm ◽  
Hermite Normal Form

Random size trees on the one and two dimensional integer lattice

1969 ◽  
Vol 6 (2) ◽  
pp. 301-308
Author(s):  
A.M.V. Verhagen
Keyword(s):  
Stochastic Process ◽  
Continuous Distribution ◽  
Integer Lattice ◽  
Two Dimensional ◽  
Random Size ◽  
Integer Lattices ◽  
The One

A stochastic process in which any tree in a forest planted on an integer lattice eliminates its four neighbours when it exceeds their heights, is studied for the case when all heights are independent samples from a continuous distribution. The proportion of the trees of the forest eliminated in this manner is determined for both the one and the two dimensional integer lattices.

scholarly journals On random nonsingular Hermite Normal Form

2016 ◽  
Vol 164 ◽  
pp. 66-86 ◽  
Author(s):  
Gengran Hu ◽  
Yanbin Pan ◽  
Renzhang Liu ◽  
Yuyun Chen
Keyword(s):  
Normal Form ◽  
Hermite Normal Form

scholarly journals Bricklaying and the Hermite Normal Form

1993 ◽  
Vol 100 (3) ◽  
pp. 242 ◽  
Author(s):  
William J. Gilbert
Keyword(s):  
Normal Form ◽  
Hermite Normal Form

EXACT GENERATION OF MINIMAL ACYCLIC DETERMINISTIC FINITE AUTOMATA

2008 ◽  
Vol 19 (04) ◽  
pp. 751-765 ◽  
Author(s):  
MARCO ALMEIDA ◽  
NELMA MOREIRA ◽  
ROGÉRIO REIS
Keyword(s):  
Normal Form ◽  
Lower Bounds ◽  
Finite Automata ◽  
Canonical Representation ◽  
Upper And Lower Bounds ◽  
Generation Algorithm ◽  
Deterministic Finite Automata

We give a canonical representation for minimal acyclic deterministic finite automata (MADFA) with n states over an alphabet of k symbols. Using this normal form, we present a method for the exact generation of MADFAs. This method avoids a rejection phase that would be needed if a generation algorithm for a larger class of objects that contains the MADFAs were used. We give upper and lower bounds for MADFAs enumeration and some exact formulas for small values of n.

Diarrhea and Malabsorption

2014 ◽  
pp. 719-733
Author(s):  
Molly L. Perencevich ◽  
Robert S. Burakoff
Keyword(s):  
United States ◽  
Normal Form ◽  
Acute Diarrhea ◽  
Chronic Diarrhea ◽  
The United States ◽  
Persistent Diarrhea ◽  
Stool Weight ◽  
General Management ◽  
Definition Of

The objective definition of diarrhea is stool weight 〉200 g per day. The more common subjective definition is frequency of defecation that is greater than or equal to three stools per day combined with less-than-normal form and consistency. Diarrhea is also defined by duration. Acute diarrhea is defined as 〈2 weeks in duration, persistent diarrhea between 2 and 4 weeks, and chronic diarrhea more than 4 weeks in duration. In the United States most cases of acute diarrhea are due to infections and are self-limited. Noninfectious etiologies are more common in chronic diarrhea. The evaluation and general management of acute and chronic diarrhea are discussed in this chapter.

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