Minimal generator of a non-deterministic operator

2019 ◽  
pp. 396-399
Author(s):  
A. Mora ◽  
P. Cordero ◽  
M. Enciso ◽  
I. P. de Guzmán
Keyword(s):  
Minimal Generator

scholarly journals On modules of finite projective dimension

2015 ◽  
Vol 219 ◽  
pp. 87-111 ◽  
Author(s):  
S. P. Dutta
Keyword(s):  
Local Ring ◽  
Projective Dimension ◽  
Order Ideal ◽  
Local Rings ◽  
Minimal Generator ◽  
Finite Projective Dimension ◽  
Special Cases ◽  
Nonzero Divisor ◽  
Finitely Generated Modules ◽  
Minimal Generators

AbstractWe address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ringRof mixed characteristicp> 0, wherepis a nonzero divisor, ifIis an ideal of finite projective dimension overRandp𝜖Iorpis a nonzero divisor onR/I, then every minimal generator ofIis a nonzero divisor. Hence, ifPis a prime ideal of finite projective dimension in a local ringR, then every minimal generator ofPis a nonzero divisor inR.

About the Lossless Reduction of the Minimal Generator Family of a Context

2007 ◽  
pp. 130-150 ◽  
Author(s):  
Tarek Hamrouni ◽  
Petko Valtchev ◽  
Sadok Ben Yahia ◽  
Engelbert Mephu Nguifo
Keyword(s):  
Minimal Generator

An Analytical Survey of Current Approaches to Mining Logical Rules from Data

2013 ◽  
pp. 71-101
Author(s):  
Xenia Naidenova
Keyword(s):  
Lattice Structure ◽  
Frequent Itemsets ◽  
Classification Rules ◽  
Functional Dependencies ◽  
Minimal Generator ◽  
Main Current ◽  
Key Concepts ◽  
Logical Rules ◽  
Classification Test

An analytical survey of some efficient current approaches to mining all kind of logical rules is presented including implicative and functional dependencies, association and classification rules. The interconnection between these approaches is analyzed. It is demonstrated that all the approaches are equivalent with respect to using the same key concepts of frequent itemsets (maximally redundant or closed itemset, generator, non-redundant or minimal generator, classification test) and the same procedures of their lattice structure construction. The main current tendencies in developing these approaches are considered.

scholarly journals On the Calculation of Formal Concept Stability

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hui-lai Zhi
Keyword(s):  
Algorithmic Complexity ◽  
Exclusion Principle ◽  
Formal Concept ◽  
Minimal Set ◽  
Minimal Generator ◽  
Critical Term ◽  
Irreducible Elements

The idea of stability has been used in many applications. However, computing stability is still a challenge and the best algorithms known so far have algorithmic complexity quadratic to the size of the lattice. To improve the effectiveness, a critical term is introduced in this paper, that is, minimal generator, which serves as the minimal set that makes a concept stable when deleting some objects from the extent. Moreover, by irreducible elements, minimal generator is derived. Finally, based on inclusion-exclusion principle and minimal generator, formulas for the calculation of concept stability are proposed.

scholarly journals On modules of finite projective dimension

2015 ◽  
Vol 219 ◽  
pp. 87-111
Author(s):  
S. P. Dutta
Keyword(s):  
Local Ring ◽  
Projective Dimension ◽  
Order Ideal ◽  
Local Rings ◽  
Minimal Generator ◽  
Finite Projective Dimension ◽  
Special Cases ◽  
Nonzero Divisor ◽  
Finitely Generated Modules ◽  
Minimal Generators

AbstractWe address two aspects of finitely generated modules of finite projective dimension over local rings and their connection in between: embeddability and grade of order ideals of minimal generators of syzygies. We provide a solution of the embeddability problem and prove important reductions and special cases of the order ideal conjecture. In particular, we derive that, in any local ring R of mixed characteristic p > 0, where p is a nonzero divisor, if I is an ideal of finite projective dimension over R and p 𝜖 I or p is a nonzero divisor on R/I, then every minimal generator of I is a nonzero divisor. Hence, if P is a prime ideal of finite projective dimension in a local ring R, then every minimal generator of P is a nonzero divisor in R.

ON THE BURNSIDE SEMIGROUPS xn = xn+m

1996 ◽  
Vol 06 (02) ◽  
pp. 179-227 ◽  
Author(s):  
ALAIR PEREIRA DO LAGO
Keyword(s):  
Word Problem ◽  
Maximal Subgroups ◽  
Substantial Part ◽  
Minimal Generator ◽  
Rewriting System ◽  
The Stability ◽  
Elementary Concept ◽  
Congruence Classes

In this paper we prove that the congruence classes of A* associated to the Burnside semigroup with |A| generators defined by the equation xn=xn+m, for n≥4 and m≥1, are recognizable. This problem was originally formulated by Brzozowski in 1969 for m=1 and n≥2. De Luca and Varricchio solved the problem for n≥5 in 90. A little later, McCammond extended the problem for m≥1 and solved it independently in the cases n≥6 and m≥1. Our work, which is based on the techniques developed by de Luca and Varricchio, extends both these results. We effectively construct a minimal generator Σ of our congruence. We introduce an elementary concept, namely the stability of productions, which allows to eliminate all hypothesis related to the values of n and m. A substantial part of our proof consists of showing that all productions in Σ are stable, for n≥4 and m≥1. We also show that Σ is a Church-Rosser rewriting system, thus solving the word problem, and show that the semigroup is finite [Formula: see text]-above. We prove that the frame of the ℛ-classes of the semigroup is a tree. We characterize and calculate the ℛ-classes, ℋ-classes and the [Formula: see text]-classes of the semigroup, regular or not, and prove that its maximal subgroups are cyclic of order m whenever all productions of Σ are stable. Recently Guba extended the cases in which the conjecture holds to n≥3 and m≥1. Using his work we obtain the stability of the productions of Σ for n=3 and m≥1 too and, hence, all properties about the semigroup structure hold in this case.

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