site stats

On primitivity of sets of matrices

Web4 de jun. de 2013 · In this paper, we analyze the computational complexity of deciding if a given set of matrices is primitive and we derive bounds on the length of the shortest … WebAbstract. For an -tuple of nonnegative matrices , primitivity/Hurwitz primitivity means the existence of a positive product/Hurwitz product, respectively (all products are with repetitions permitted). The Hurwitz product with a Parikh vector is the sum of all products with multipliers , . Ergodicity/Hurwitz ergodicity means the existence of the corresponding …

The Synchronizing Probability Function for Primitive Sets of …

Webprimitivity of one matrix (see, for instance [12, chapter 8]). However, for a set of matrices A 1 ,...,A k the situation is more difficult: instead of working with powers of one matrix, we Web25 de fev. de 2024 · B. Liu, “Generalized Exponents of Boolean Matrices,” Linear Algebra Appl. 373, 169–182 (2003). Article MathSciNet MATH Google Scholar Z. Miao and K. Zhang, “The Local Exponent Sets of Primitive Digraphs,” Linear … daewoo express fare list https://acebodyworx2020.com

Primitive sets of nonnegative matrices and synchronizing automata

Web10 de jul. de 2024 · Deciding whether a set is primitive is a PSPACE-complete problem for sets of two matrices , while it is an NP-hard problem for sets of at least three matrices . Computing the exponent of a primitive set is usually hard, namely it is an FP \(^{\text {NP}[\log ]}\) -complete problem [ 15 ]; for the complexity of other problems related to … WebInformación del artículo On primitivity of sets of matrices. Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Vol. 61, 2015, págs. 80-88 Idioma: inglés Texto completo no disponible (Saber más ...); Resumen. A nonnegative matrix AA is called primitive if AkAk is positive for some integer k>0k>0. WebSociety for Industrial and Applied Mathematics. 3600 Market Street, 6th Floor Philadelphia, PA 19104 USA bioadvance reviews

A Linear Bound on the K-Rendezvous Time for Primitive Sets of NZ …

Category:On primitivity of sets of matrices - ScienceDirect

Tags:On primitivity of sets of matrices

On primitivity of sets of matrices

The Synchronizing Probability Function for Primitive Sets of Matrices

WebIn this paper the primitivity of a positive matrix pair (A,B) is introduced as a strict positivity constraint on the asymptotic behavior of the associated two-dimensional (2D) state … WebGiven a square matrix A over the integers, we consider the Z-module M A generated by the set of all matrices that are permutation-similar to A.Motivated by analogous problems on signed graph decompositions and block designs, we are interested in the completely symmetric matrices a I + b J belonging to M A.We give a relatively fast method to …

On primitivity of sets of matrices

Did you know?

WebThe property of primitivity of a set of matrices is important in several applications. In particular, its presence enables one to use efficient algorithms for the computation of … Web1 de ago. de 2024 · In our approach, we use the elements of semigroups as labels to generalize the notion of primitivity and unify theorems of Section 1. Let A = {a1, a2, . . . , ak} be a ï¬ nite set of labels. Our main idea is to treat A as elements of a semigroup. Let A∗ be the free semigroup generated by A: its elements are words over A and the the ...

WebWe pay special attention to the set of matrices without zero rows and columns, denoted by $\mathscr{NZ}$, due to its intriguing connections to the Cerný conjecture. We rely on synchronizing automata theory to derive a number of results about primitive sets of matrices. Making use of an asymptotic estimate by Rystsov ... WebMotivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Černý conjecture by studying the …

Web1 contains the set of stochastic matrices while NZ 2 contains the set of doubly 101 stochastic matrices. 102 A matrix is an automaton matrix if it is a zero-one matrix each row of which 103 contains a unique one. We denote by A the set of all automaton matrices, which is 104 an important subclass of NZ 1. An automaton of size nis a subset of ...

Web10 de jul. de 2024 · Deciding whether a set is primitive is a PSPACE-complete problem for sets of two matrices , while it is an NP-hard problem for sets of at least three matrices . …

WebThe property of primitivity ofa set of matrices is impor-tant in several applications. In particular, its presence enables one to use efficient algorithms for the computa-tion of … bioadvanced weed and feed instructionsWebtheir names. Mimicking their terminology, we call the exponent of a primitive set Mthe length of its shortest positive product, and we indicate it by exp(M). The primitivity property of nonnegative matrix sets has lately found applica-tions in various elds as in consensus of discrete-time multi-agent systems [7], in bio advance international bangladeshWeb1 de ago. de 2024 · In our approach, we use the elements of semigroups as labels to generalize the notion of primitivity and unify theorems of Section 1. Let A = {a1, a2, . . . … bioadvanced tree and shrub when to apply