AN ALGEBRAIC THEORY FOR REGULAR LANGUAGES OF FINITE AND INFINITE WORDS

1993 ◽  
Vol 03 (04) ◽  
pp. 447-489 ◽  
Author(s):  
THOMAS WILKE
Keyword(s):  
Algebraic Theory ◽  
Algebraic Approach ◽  
Regular Languages ◽  
Cantor Space ◽  
Infinite Words ◽  
Finite Semigroups ◽  
Borel Hierarchy ◽  
Algebraic Description ◽  
One To One

An algebraic approach to the theory of regular languages of finite and infinite words (∞-languages) is presented. It extends the algebraic theory of regular languages of finite words, which is based on finite semigroups. Their role is taken over by a structure called right binoid. A variety theorem is proved: there is a one-to-one correspondence between varieties of ∞-languages and pseudovarieties of right binoids. The class of locally threshold testable languages and several natural subclasses (such as the class of locally testable languages) as well as classes of the Borel hierarchy over the Cantor space (restricted to regular languages) are investigated as examples for varieties of ∞-languages. The corresponding pseudovarieties of right binoids are characterized and in some cases defining equations are derived. The connections with the algebraic description and classification of regular languages of infinite words in terms of finite semigroups are pointed out.

An Algebraic Approach to Weakly Symmetric Finsler Spaces

2010 ◽  
Vol 62 (1) ◽  
pp. 52-73 ◽  
Author(s):  
Shaoqiang Deng
Keyword(s):  
Large Class ◽  
Lie Algebras ◽  
Algebraic Approach ◽  
Comparison Theorems ◽  
Finsler Spaces ◽  
Volume Comparison ◽  
Algebraic Description ◽  
Interesting Class ◽  
Weakly Symmetric

AbstractIn this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann-Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions 2 and 3. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. Thismeans that reversible non-Berwaldian Finsler spaces with vanishing S-curvaturemay exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces.

Fuzzy regular languages over finite and infinite words

2006 ◽  
Vol 157 (11) ◽  
pp. 1532-1549 ◽  
Author(s):  
Werner Kuich ◽  
George Rahonis
Keyword(s):  
Regular Languages ◽  
Infinite Words

THE DYNAMICS OF NQ-SYSTEMS IN THE PLANE

2009 ◽  
Vol 19 (01) ◽  
pp. 117-133 ◽  
Author(s):  
MATEJ MENCINGER ◽  
MILAN KUTNJAK
Keyword(s):  
Algebraic Approach ◽  
Dynamical Analysis ◽  
Algebraic Classification ◽  
Commutative Algebras ◽  
Planar Maps ◽  
Points Of View ◽  
One To One

The dynamics of discrete homogeneous quadratic planar maps is considered via the algebraic approach. There is a one-to-one correspondence between these systems and 2D commutative algebras (c.f. [Markus, 1960]). In particular, we consider the systems corresponding to algebras which contain some nilpotents of rank two (i.e. NQ-systems). Markus algebraic classification is used to obtain the class representatives. The case-by-case dynamical analysis is presented. It is proven that there is no chaos in NQ-systems. Yet, some cases are really interesting from the dynamical and bifurcational points of view.

Algebraic Theory of Recombination Spaces

1997 ◽  
Vol 5 (3) ◽  
pp. 241-275 ◽  
Author(s):  
Peter F. Stadler ◽  
Günter P. Wagner
Keyword(s):  
Nearest Neighbor ◽  
Fitness Landscape ◽  
Algebraic Theory ◽  
Algebraic Approach ◽  
Search Space ◽  
Space Structure ◽  
Fitness Landscapes ◽  
Mathematical Representation ◽  
Laplacian Operator ◽  
Fourier Decomposition

A new mathematical representation is proposed for the configuration space structure induced by recombination, which we call “P-structure.” It consists of a mapping of pairs of objects to the power set of all objects in the search space. The mapping assigns to each pair of parental “genotypes” the set of all recombinant genotypes obtainable from the parental ones. It is shown that this construction allows a Fourier decomposition of fitness landscapes into a superposition of “elementary landscapes.” This decomposition is analogous to the Fourier decomposition of fitness landscapes on mutation spaces. The elementary landscapes are obtained as eigenfunctions of a Laplacian operator defined for P-structures. For binary string recombination, the elementary landscapes are exactly the p-spin functions (Walsh functions), that is, the same as the elementary landscapes of the string point mutation spaces (i.e., the hypercube). This supports the notion of a strong homomorphism between string mutation and recombination spaces. However, the effective nearest neighbor correlations on these elementary landscapes differ between mutation and recombination and among different recombination operators. On average, the nearest neighbor correlation is higher for one-point recombination than for uniform recombination. For one-point recombination, the correlations are higher for elementary landscapes with fewer interacting sites as well as for sites that have closer linkage, confirming the qualitative predictions of the Schema Theorem. We conclude that the algebraic approach to fitness landscape analysis can be extended to recombination spaces and provides an effective way to analyze the relative hardness of a landscape for a given recombination operator.

scholarly journals Classification of fused links

2016 ◽  
Vol 25 (14) ◽  
pp. 1650076 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Symmetric Group ◽  
Equivalence Classes ◽  
One To One ◽  
Text Component

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of [Formula: see text]-component fused links is in one-to-one correspondence with the set of elements of the abelization [Formula: see text] up to conjugation by elements from the symmetric group [Formula: see text].

The trichotomic machine

Semiotica ◽  
2019 ◽  
Vol 2019 (228) ◽  
pp. 173-192 ◽  
Author(s):  
Robert Marty
Keyword(s):  
Formal Analysis ◽  
Homological Algebra ◽  
Algebraic Theory ◽  
Hierarchical Structures ◽  
Additional Benefit ◽  
General Methodology ◽  
New Methodologies ◽  
Basic Concepts ◽  
Categories And Functors

AbstractThe formal analysis of the principles leading the classification of the hexadic, decadic, and triadic signs from C. S. Peirce especially, gives rise to a general methodology allowing to systematically classify any n-adic combinatory named “protosign.” Basic concepts of the algebraic theory regarding the categories and functors will be used. That formalization provides an additional benefit by highlighting and systematizing formal immanent relationships between the classes of protosigns (or signs). Well known hierarchical structures (lattices) are then obtained. Thanks to the contribution of specific concepts in the Homological Algebra, new methodologies of analysis and creation of significations can be introduced.

FINITE STATE PROCESSES, Z-TEMPORAL LOGIC AND THE MONADIC THEORY OF THE INTEGERS

1992 ◽  
Vol 03 (03) ◽  
pp. 233-244 ◽  
Author(s):  
A. SAOUDI ◽  
D.E. MULLER ◽  
P.E. SCHUPP
Keyword(s):  
Temporal Logic ◽  
Linear Temporal Logic ◽  
Second Order ◽  
Regular Languages ◽  
Infinite Words ◽  
First Order ◽  
Monadic Theory ◽  
Finite State ◽  
Temporal Formula

We introduce four classes of Z-regular grammars for generating bi-infinite words (i.e. Z-words) and prove that they generate exactly Z-regular languages. We extend the second order monadic theory of one successor to the set of the integers (i.e. Z) and give some characterizations of this theory in terms of Z-regular grammars and Z-regular languages. We prove that this theory is decidable and equivalent to the weak theory. We also extend the linear temporal logic to Z-temporal logic and then prove that each Z-temporal formula is equivalent to a first order monadic formula. We prove that the correctness problem for finite state processes is decidable.

HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY

1990 ◽  
Vol 02 (01) ◽  
pp. 105-125 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
HANNS SCHULZ-MIRBACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Algebraic Approach ◽  
Energy Tensor ◽  
Quantum Field ◽  
Haag Duality ◽  
Conformal Fields ◽  
Stress Energy

Haag duality is established in conformal quantum field theory for observable fields on the compactified light ray S1 and Minkowski space S1×S1, respectively. This result provides the foundation for an algebraic approach to the classification of conformal theories. Haag duality can fail, however, for the restriction of conformal fields to the underlying non-compact spaces ℝ, respectively ℝ×ℝ. A prominent example is the stress energy tensor with central charge c>1.

Translation semantic variability: How semantic relatedness affects learning of translation-ambiguous words

2016 ◽  
Vol 20 (4) ◽  
pp. 783-794 ◽  
Author(s):  
JENNIFER BRACKEN ◽  
TAMAR DEGANI ◽  
CHELSEA EDDINGTON ◽  
NATASHA TOKOWICZ
Keyword(s):  
Language Learning ◽  
Word Learning ◽  
Ambiguous Word ◽  
Semantic Relatedness ◽  
Continuous Measure ◽  
Unique Variance ◽  
Ambiguous Words ◽  
One To One ◽  
Dichotomous Classification

Translations often do not align directly across languages, and indirect mappings reduce the accuracy of language learning. To facilitate examination of this issue, we developed a new continuous measure for quantifying the semantic relatedness of words with more than one translation (hereafter translation-ambiguous words). Participants rated the similarity of each translation to every other translation, yielding a Translation Semantic Variability (TSV) score, ranging from 1.00 (unrelated) to 7.00 (related). Then, we determined how relatedness between translations affects translation-ambiguous word learning from German to English. German words with low TSV scores were recognized as translations more slowly and less accurately than German words with high TSV scores. TSV explains unique variance beyond the previously-used dichotomous classification of words as form vs. meaning ambiguous. We propose that the relatedness of the translation alternatives influences learning because it affects the ease with which a one-to-one mapping can be established between form and meaning.

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