Relevant bibliographies by topics / Regular polynomial

Academic literature on the topic 'Regular polynomial'

Author: Grafiati
Published: 26 October 2022

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Regular polynomial":

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Merikoski, Jorma K. "Regular polygons, Morgan-Voyce polynomials, and Chebyshev polynomials." Notes on Number Theory and Discrete Mathematics 27, no. 2 (June 2021): 79–87. http://dx.doi.org/10.7546/nntdm.2021.27.2.79-87.

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We say that a monic polynomial with integer coefficients is a polygomial if its each zero is obtained by squaring the edge or a diagonal of a regular n-gon with unit circumradius. We find connections of certain polygomials with Morgan-Voyce polynomials and further with Chebyshev polynomials of second kind.
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Lee, Jae-Ho. "Nonsymmetric Askey–Wilson polynomials and Q -polynomial distance-regular graphs." Journal of Combinatorial Theory, Series A 147 (April 2017): 75–118. http://dx.doi.org/10.1016/j.jcta.2016.11.006.

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Carballosa, Walter, José M. Rodríguez, José M. Sigarreta, and Yadira Torres-Nuñez. "Alliance polynomial of regular graphs." Discrete Applied Mathematics 225 (July 2017): 22–32. http://dx.doi.org/10.1016/j.dam.2017.03.016.

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Meleshkin, A. V. "Regular semigroups of polynomial growth." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 2 (February 1990): 152–58. http://dx.doi.org/10.1007/bf01156824.

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Berthomieu, Jérémy, Jean-Charles Faugère, and Ludovic Perret. "Polynomial-time algorithms for quadratic isomorphism of polynomials: The regular case." Journal of Complexity 31, no. 4 (August 2015): 590–616. http://dx.doi.org/10.1016/j.jco.2015.04.001.

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Dickie, Garth A. "Twice Q-Polynomial Distance-Regular Graphs." Journal of Combinatorial Theory, Series B 68, no. 1 (September 1996): 161–66. http://dx.doi.org/10.1006/jctb.1996.0061.

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Golasiński, Marek, and Francisco Gómez Ruiz. "Polynomial and Regular Maps into Grassmannians." K-Theory 26, no. 1 (May 2002): 51–68. http://dx.doi.org/10.1023/a:1016305323458.

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Caughman IV, John S. "Bipartite Q -Polynomial Distance-Regular Graphs." Graphs and Combinatorics 20, no. 1 (March 1, 2004): 47–57. http://dx.doi.org/10.1007/s00373-003-0538-8.

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Galetto, Federico, Anthony Vito Geramita, and David Louis Wehlau. "Degrees of Regular Sequences With a Symmetric Group Action." Canadian Journal of Mathematics 71, no. 03 (January 7, 2019): 557–78. http://dx.doi.org/10.4153/cjm-2017-035-3.

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AbstractWe consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible isomorphism types for these ideals. Following up on that work, we now analyze the possible degrees of the elements in such regular sequences. For each case of our classification, we provide some criteria guaranteeing the existence of regular sequences in certain degrees.
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Birget, J. C. "Semigroups and one-way functions." International Journal of Algebra and Computation 25, no. 01n02 (February 2015): 3–36. http://dx.doi.org/10.1142/s0218196715400019.

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We study the complexity classes 𝖯 and 𝖭𝖯 through a semigroup 𝖿𝖯 ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. The semigroup 𝖿𝖯 is non-regular if and only if 𝖯 ≠ 𝖭𝖯. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are exactly the non-regular elements of 𝖿𝖯. We prove various properties of 𝖿𝖯, e.g. that it is finitely generated. We define reductions with respect to which certain universal one-way functions are 𝖿𝖯-complete.
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Journal articles

Dissertations / Theses on the topic "Regular polynomial":

1

Moreira, Joel Moreira. "Partition regular polynomial patterns in commutative semigroups." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1467131194.

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Molina, Aristizabal Sergio D. "Semi-Regular Sequences over F2." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1445342810.

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Mehrabdollahei, Mahya. "La mesure de Mahler d’une famille de polynômes exacts." Thesis, Sorbonne université, 2022. https://accesdistant.sorbonne-universite.fr/login?url=https://theses-intra.sorbonne-universite.fr/2022SORUS170.pdf.

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Dans cette thèse, nous étudions la suite de mesures de Mahler d’une famille de polynômes à deux variables exacts et réguliers, que nous notons Pd := P0≤i+j≤d xiyj . Elle n’est bornée ni en volume, ni en genre de la courbe algébrique sous-jacente. Nous obtenons une expression pour la mesure de Mahler de Pd comme somme finie de valeurs spéciales du dilogarithme de Bloch-Wigner. Nous utilisons SageMath pour approximer m(Pd) pour 1 ≤ d ≤ 1000. En recourant à trois méthodes différentes, nous prouvons que la limite de la suite de mesures de Mahler de cette famille converge vers 92π2 ζ(3). De plus, nous calculons le développement asymptotique de la mesure de Mahler de Pd et prouvons que sa vitesse de convergence est de O(log dd2 ). Nous démontrons également une généralisation du théorème de Boyd-Lawton, affirmant que les mesures de Mahler multivariées peuvent être approximéess en utilisant les mesures de Mahler de dimension inférieure. Enfin, nous prouvons que la mesure de Mahler de Pd pour d arbitraire peut être écrite comme une combinaison linéaire de fonctions L associées à un caractère de Dirichlet primitif impair. Nous calculons finalement explicitement la représentation de la mesure de Mahler de Pd en termes de fonctions L, pour 1 ≤ d ≤ 6
In this thesis we investigate the sequence of Mahler measures of a family of bivariate regular exact polynomials, called Pd := P0≤i+j≤d xiyj , unbounded in both degree and the genus of the algebraic curve. We obtain a closed formula for the Mahler measure of Pd in termsof special values of the Bloch–Wigner dilogarithm. We approximate m(Pd), for 1 ≤ d ≤ 1000,with arbitrary precision using SageMath. Using 3 different methods we prove that the limitof the sequence of the Mahler measure of this family converges to 92π2 ζ(3). Moreover, we compute the asymptotic expansion of the Mahler measure of Pd which implies that the rate of the convergence is O(log dd2 ). We also prove a generalization of the theorem of the Boyd-Lawton which asserts that the multivariate Mahler measures can be approximated using the lower dimensional Mahler measures. Finally, we prove that the Mahler measure of Pd, for arbitrary d can be written as a linear combination of L-functions associated with an odd primitive Dirichlet character. In addition, we compute explicitly the representation of the Mahler measure of Pd in terms of L-functions, for 1 ≤ d ≤ 6
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Lopes, Aislan Sirino. "CritÃrio para a construtibilidade de polÃgonos regulares por rÃgua e compasso e nÃmeros construtÃveis." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12590.

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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Este trabalho aborda construÃÃes geomÃtricas elementares e de polÃgonos regulares realizadas com rÃgua nÃo graduada e compasso respeitando as regras ou operaÃÃes elementares usadas na Antiguidade pelos gregos. Tais construÃÃes serÃo inicialmente tratadas de uma forma puramente geomÃtrica e, a fim de encontrar um critÃrio que possa determinar a possibilidade de construÃÃo de polÃgonos regulares, passarÃo a ser discutidas por um viÃs algÃbrico. Este tratamento algÃbrico evidenciarà uma relaÃÃo entre a geometria e a Ãlgebra, em especial, a relaÃÃo entre os vÃrtices de um polÃgono regular e as raÃzes de polinÃmios de uma variÃvel com coeficientes racionais. Este tratamento algÃbrico nos levarà naturalmente ao conceito de construtibilidade de nÃmeros e pontos no plano de um corpo, o que exigirà o uso de extensÃes algÃbricas de corpos, e os critÃrios para a construtibi- lidade destes nos levarà a um critÃrio de construtibilidade dos polÃgonos pretendidos.
This work discusses basic geometric constructions and constructions of regular polygons with ruler and compass made respecting the rules or elementary operations used by the ancient Greeks. Such constructs are initially treated in a purely geometric form and, in order to find a criterion that can determine the possibility of construction of regular polygons, will be discussed by an algebraic bias. This algebraic treatment will show a relationship between geometry and algebra, in particular, the relationship between the vertices of a regular polygon and the roots of polynomials in a variable with rational coefficients. This algebraic treatment leads us naturally to the concept of constructibility of numbers and points in a field, which will require the use of algebraic field extensions, and the criteria for the constructibility of these leads to a criterion for constructibility of polygons.
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Cruz, Carla Maria. "Numerical and combinatorial applications of generalized Appell polynomials." Doctoral thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/13962.

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Doutoramento em Matemática
This thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the construction of new bases for the space of homogeneous holomorphic polynomials whose elements are all isomorphic to the integer powers of the complex variable. For this reason, such polynomials are called pseudo-complex powers (PCP). Different variants of them are subject of a detailed investigation. Special attention is paid to the numerical aspects of PCP. An efficient algorithm based on complex arithmetic is proposed for their implementation. In this context a brief survey on numerical methods for inverting Vandermonde matrices is presented and a modified algorithm is proposed which illustrates advantages of a special type of PCP. Finally, combinatorial applications of generalized Appell polynomials are emphasized. The explicit expression of the coefficients of a particular type of Appell polynomials and their relation to a Pascal simplex with hypercomplex entries are derived. The comparison of two types of 3D Appell polynomials leads to the detection of new trigonometric summation formulas and combinatorial identities of Riordan-Sofo type characterized by their expression in terms of central binomial coefficients.
Esta tese estuda propriedades e aplicações de diferentes polinómios de Appell generalizados no contexto da análise de Clifford. Exemplificando uma transformação realizada por polinómios de Appell generalizados, é introduzida uma transformação análoga à transformação de Joukowski complexa de ordem dois. A análise de um n- simplex de Pascal com entradas hipercomplexas permite sublinhar a relevância combinatória de polinómios hipercomplexos de Appell. O conceito de variáveis totalmente regulares e a sua relação com polinómios de Appell generalizados conduz à construção de novas bases para o espaço dos polinómios homogéneos holomorfos cujos elementos são todos isomorfos às potências inteiras da variável complexa. Por este motivo, tais polinómios são chamados de potências pseudo-complexas (PCP). Diferentes variantes de PCP são objeto de uma investigação detalhada. É dada especial atenção aos aspectos numéricos de PCP. Um algoritmo eficiente baseado em aritmética complexa é proposto para a sua implementação. Neste contexto, é apresentado um breve resumo de métodos numéricos para inverter matrizes de Vandermonde e é proposto um algoritmo modificado para ilustrar as vantagens de um tipo especial de PCP. Finalmente, são enfatizadas aplicações combinatórias de polinómios de Appell generalizados. A expressão explícita dos coeficientes de um tipo particular de polinómios de Appell e a sua relação com um simplex de Pascal com entradas hipercomplexas são obtidas. A comparação de dois tipos de polinómios de Appell tridimensionais leva à deteção de novas fórmulas envolvendo somas trigonométricas e de identidades combinatórias do tipo de Riordan – Sofo, caracterizadas pela sua expressão em termos de coeficientes binomiais centrais.
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Szumowicz, Anna Maria. "Regular representations of GLn( O) and the inertial Langlands correspondence." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS360.

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Cette thèse contient deux parties. La première porte sur la théorie des représentations des groupes p-adiques. Le but est de trouver de nouvelles informations et de nouveaux invariants des types cuspidaux de groupes linéaires généraux. Soit F un corps local non archimédien et soit OF son anneau des entiers. Nous décrivons les types cuspidaux sur GLp(OF ) (où p est un nombre premier) en termes d’orbites. Nous déterminons quels types cuspidaux sont réguliers et donnons un exemple qui montre que l’orbite de la représentation ne suffit pas à déterminer si la représentation est un type cuspidal ou non. Nous montrons qu’un type cuspidal pour une représentation π de GLp(F) est régulier si et seulement si le niveau normalisé de π est égal à m ou m − 1 p pour un certain m ∈ Z. La deuxième partie porte sur les polynômes à valeurs entières, les p-rangements simultanés (au sens de Bhargava) et l’équidistribution dans les corps des nombres. C’est un projet joint avec Mikołaj Frączyk. La notion de p-rangement provient des travaux de Bhargava sur les polynômes à valeurs entières. Soit k un corps de nombres et soit Ok son anneau des entiers. Une suite d’éléments de Ok est un p-rangement simultané si elle est équidistribuée modulo tous les idéaux premières de Ok du mieux possible. Nous prouvons que le seul corps de nombres k tel que Ok admette des p-rangements simultanés est Q
This thesis is divided into two parts. The first one comes from the representation theory of reductive p-adic groups. The main motivation behind this part of the thesis is to find new explicit information and invariants of the types in general linear groups. Let F be a nonArchimedean local field and let OF be its ring of integers. We give an explicit description of cuspidal types on GLp(OF ), with p prime, in terms of orbits. We determine which of them are regular representations and we provide an example which shows that an orbit of a representation does not always determine whether it is a cuspidal type or not. At the same time we prove that a cuspidal type for a representation π of GLp(F) is regular if and only if the normalised level of π is equal to m or m − 1 p for m ∈ Z. The second part of the thesis comes from the theory of integer-valued polynomials and simultaneous p-orderings. This is a joint work with Mikołaj Frączyk. The notion of simultaneous p-ordering was introduced by Bhargava in his early work on integer-valued polynomials. Let k be a number field and let Ok be its ring of integers. Roughly speaking a simultaneous p-ordering is a sequence of elements from Ok which is equidistributed modulo every power of every prime ideal in Ok as well as possible. Bhargava asked which subsets of Dedekind domains admit simultaneous p-ordering. Together with Mikołaj Frączyk we proved that the only number field k with Ok admitting a simultaneous p-ordering is Q
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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrö
dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
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Lang, Stanislav. "Řešení spojitých systémů evolučními výpočetními technikami." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-371772.

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The thesis deals the issue of solution of continuous systems by evolutionary computational techniques. Evolutionary computing techniques fall into the field of softcomputing, an advanced metaheuristics optimization that is becoming more and more a method of solving complicated optimization problems with the gradual increase in computing performance of computers. The solution of continuous systems, or the synthesis of continuous control circuits, is one of the areas where these advanced algorithms find their application. When dealing with continuous systems we will focus on regulatory issues. Evolutionary computing can then become a tool not only for optimization of controller parameters but also to design its structure. Various algorithms (genetic algorithm, differential evolution, etc.) can be used to optimize the parameters of the controller, for the design of the controller structurewe usually encounter so called grammatical evolution. However, the use of grammatical evolution is not necessary if appropriate coding is used, as suggested in the presented thesis. The thesis presents a method of designing the structure and parameters of a general linear controller using the genetic algorithm. A general linear regulator is known also as so called polynomial controller, if we encounter the polynomial theory of control. The method of encoding the description of the general linear controller into the genetic chain is crucial, it determines a set of algorithms that are usable for optimization and influence the efficiency of the calculations. Described coding, effective EVT implementation, including multi-criteria optimization, is a key benefit of this work.
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Kratz, Marie. "Some contributions in probability and statistics of extremes." Habilitation à diriger des recherches, Université Panthéon-Sorbonne - Paris I, 2005. http://tel.archives-ouvertes.fr/tel-00239329.

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PENG, CHIEN-NAN, and 彭健男. "Multilinear Polynomials with Regular or Nilpotent Values." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/28442073956068464235.

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Books on the topic "Regular polynomial":

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Yakubov, S. Completeness of root functions of regular differential operators. Essex, England: Longman Scientific & Technical, 1994.

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Sheehan, Daniel Dean. Interpolating a regular grid of elevations from random points using three algorithms: Kriging, splines, and polynomial surfaces. 1987.

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Algebraic And Combinatorial Aspects Of Tropical Geometry Ciem Workshop On Tropical Geometry December 1216 2011 International Center For Mathematical Meetings Castro Urdiales Spain. American Mathematical Society, 2013.

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Book chapters on the topic "Regular polynomial":

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Brouwer, Andries E., Arjeh M. Cohen, and Arnold Neumaier. "Q-polynomial Distance-Regular Graphs." In Distance-Regular Graphs, 235–54. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-74341-2_8.

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Piponi, Dan, and Brent A. Yorgey. "Polynomial Functors Constrained by Regular Expressions." In Lecture Notes in Computer Science, 113–36. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19797-5_6.

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Szilard, Andrew, Sheng Yu, Kaizhong Zhang, and Jeffrey Shallit. "Characterizing regular languages with polynomial densities." In Mathematical Foundations of Computer Science 1992, 494–503. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55808-x_48.

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Klíma, Ondřej, and Libor Polák. "Polynomial Operators on Classes of Regular Languages." In Algebraic Informatics, 260–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-03564-7_17.

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Mortini, Raymond, and Rudolf Rupp. "Polynomial, Noetherian, and von Neumann regular rings." In Extension Problems and Stable Ranks, 1153–94. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73872-3_22.

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Salahi, Maziar, and Tamás Terlaky. "Self-Regular Interior-Point Methods for Semidefinite Optimization." In Handbook on Semidefinite, Conic and Polynomial Optimization, 437–54. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-1-4614-0769-0_15.

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Bochnak, Jacek, Michel Coste, and Marie-Françoise Roy. "Polynomial or Regular Mappings with Values in Spheres." In Real Algebraic Geometry, 339–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03718-8_14.

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Weispfenning, Volker. "Gröbner bases for polynomial ideals over commutative regular rings." In Lecture Notes in Computer Science, 336–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51517-8_137.

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Case, John, Sanjay Jain, Rüdiger Reischuk, Frank Stephan, and Thomas Zeugmann. "Learning a Subclass of Regular Patterns in Polynomial Time." In Lecture Notes in Computer Science, 234–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-39624-6_19.

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Angluin, Dana, Timos Antonopoulos, Dana Fisman, and Nevin George. "Representing Regular Languages of Infinite Words Using Mod 2 Multiplicity Automata." In Lecture Notes in Computer Science, 1–20. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-99253-8_1.

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AbstractWe explore the suitability of mod 2 multiplicity automata (M2MAs) as a representation for regular languages of infinite words. M2MAs are a deterministic representation that is known to be learnable in polynomial time with membership and equivalence queries, in contrast to many other representations. Another advantage of M2MAs compared to non-deterministic automata is that their equivalence can be decided in polynomial time and complementation incurs only an additive constant size increase. Because learning time is parameterized by the size of the representation, particular attention is focused on the relative succinctness of alternate representations, in particular, LTL formulas and Büchi automata of the types: deterministic, non-deterministic and strongly unambiguous. We supplement the theoretical results of worst case upper and lower bounds with experimental results computed for randomly generated automata and specific families of LTL formulas.

Conference papers on the topic "Regular polynomial":

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LI, YONG-BIN, JING-ZHONG ZHANG, and LU YANG. "DECOMPOSING POLYNOMIAL SYSTEMS INTO STRONG REGULAR SETS." In Proceedings of the First International Congress of Mathematical Software. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777171_0038.

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Kayal, Neeraj, Chandan Saha, and Ramprasad Saptharishi. "A super-polynomial lower bound for regular arithmetic formulas." In STOC '14: Symposium on Theory of Computing. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2591796.2591847.

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Pugh, A. C., M. Hou, and G. E. Hayton. "Input-output equivalent representation of non-regular polynomial matrix descriptions." In Proceedings of 16th American CONTROL Conference. IEEE, 1997. http://dx.doi.org/10.1109/acc.1997.610890.

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Galindo, R., and A. Herrera. "Dynamic and robust regular I/O decoupling: A polynomial approach." In 1999 European Control Conference (ECC). IEEE, 1999. http://dx.doi.org/10.23919/ecc.1999.7099522.

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Zhang, Liping, and Guoshan Zhang. "The State Response and Controllability of Regular Polynomial Matrix Systems." In 2018 37th Chinese Control Conference (CCC). IEEE, 2018. http://dx.doi.org/10.23919/chicc.2018.8482577.

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Ronca, Alessandro, and Giuseppe De Giacomo. "Efficient PAC Reinforcement Learning in Regular Decision Processes." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/279.

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Recently regular decision processes have been proposed as a well-behaved form of non-Markov decision process. Regular decision processes are characterised by a transition function and a reward function that depend on the whole history, though regularly (as in regular languages). In practice both the transition and the reward functions can be seen as finite transducers. We study reinforcement learning in regular decision processes. Our main contribution is to show that a near-optimal policy can be PAC-learned in polynomial time in a set of parameters that describe the underlying decision process. We argue that the identified set of parameters is minimal and it reasonably captures the difficulty of a regular decision process.
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Hara, Seiya, and Takayoshi Shoudai. "Polynomial Time Mat Learning of C-deterministic Regular Formal Graph Systems." In 2014 IIAI 3rd International Conference on Advanced Applied Informatics (IIAIAAI). IEEE, 2014. http://dx.doi.org/10.1109/iiai-aai.2014.51.

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Le, Huu Phuoc, and Mohab Safey El Din. "Faster One Block Quantifier Elimination for Regular Polynomial Systems of Equations." In ISSAC '21: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2021. http://dx.doi.org/10.1145/3452143.3465546.

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SATO, Y., and A. SUZUKI. "GRÖBNER BASES IN POLYNOMIAL RINGS OVER VON NEUMANN REGULAR RINGS — THEIR APPLICATIONS." In Proceedings of the Fourth Asian Symposium (ASCM 2000). WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812791962_0007.

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10

Sato, Yosuke. "A new type of canonical Gröbner bases in polynomial rings over Von Neumann regular rings." In the 1998 international symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/281508.281658.

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Reports on the topic "Regular polynomial":

1

Baader, Franz, and Ralf Küsters. Unification in a Description Logic with Transitive Closure of Roles. Aachen University of Technology, 2001. http://dx.doi.org/10.25368/2022.115.

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Abstract:
Unification of concept descriptions was introduced by Baader and Narendran as a tool for detecting redundancies in knowledge bases. It was shown that unification in the small description logic FL₀, which allows for conjunction, value restriction, and the top concept only, is already ExpTime-complete. The present paper shows that the complexity does not increase if one additionally allows for composition, union, and transitive closure of roles. It also shows that matching (which is polynomial in FL₀) is PSpace-complete in the extended description logic. These results are proved via a reduction to linear equations over regular languages, which are then solved using automata. The obtained results are also of interest in formal language theory.

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