Palindromic Characteristic of Committed Graphs and Some Model Theoretic Properties

2020 ◽  
Vol 31 (04) ◽  
pp. 483-498
Author(s):  
Ahmet Çevik
Keyword(s):  
Model Theory ◽  
Formal Language ◽  
Formal Languages ◽  
Regular Graphs

We bring into attention the interplay between model theory of committed graphs (1-regular graphs) and their palindromic characteristic in the domain of formal languages. We prove some model theoretic properties of committed graphs and then give a characterization of them in the formal language domain using palindromes. We show in the first part of the paper that the theory of committed graphs and the theory of infinite committed graphs differ in terms of completeness. We give the observation that theories of finite and infinite committed graphs are both decidable. The former is finitely axiomatizable, whereas the latter is not. We note that every committed graph is isomorphic to the structure of integers. In the second part, as our main focus of the paper and using some of the results in the first section, we give a characterization of committed graphs based on the notion of finite and infinite palindrome strings.

scholarly journals ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

2021 ◽  
pp. 1-40
Author(s):  
NICK GILL ◽  
BIANCA LODÀ ◽  
PABLO SPIGA
Keyword(s):  
Permutation Group ◽  
Model Theory ◽  
Independent Set ◽  
Maximum Size ◽  
Proper Subset ◽  
Permutation Groups ◽  
Finite Permutation Group ◽  
Pointwise Stabilizer ◽  
Relational Complexity

Abstract Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

THE DEVELOPMENT OF FORMAL LANGUAGE THEORY SINCE 1956

1990 ◽  
Vol 01 (04) ◽  
pp. 355-368
Author(s):  
ROBERT McNAUGHTON
Keyword(s):  
Formal Language ◽  
Formal Languages ◽  
Early Years ◽  
Formal Language Theory ◽  
Language Theory ◽  
Personal Interest

This brief survey will discuss the early years of the theory of formal languages through about 1970, treating only the most fundamental of the concepts. The paper will conclude with a brief discussion of a small number of topics, the choice reflecting only the personal interest of the author.

scholarly journals Characterization of two-distance sequences

1992 ◽  
Vol 53 (2) ◽  
pp. 198-218 ◽  
Author(s):  
W. F. Lunnon ◽  
P. A. B. Pleasants
Keyword(s):  
Formal Languages ◽  
Minimal Word ◽  
Beatty Sequences ◽  
Straight Lines ◽  
Symbol Sequences ◽  
Number Of Authors

AbstractThree differently defined classes of two-symbol sequences, which we call the two-distance sequences, the linear sequences and the characteristic sequences, have been discussed by a number of authors and some equivalences between them are known. We present a self-contained proof that the three classes are the same (when ambiguous cases of linear sequences are suitably in terpreted). Associated with each sequence is a real invariant (having a different appropriate definition for each of the three classes). We give results on the relation between sequences with the same invariant and on the symmetry of the sequences. The sequences are closely related to Beatty sequences and occur as digitized straight lines and quasicrystals. They also provide examples of minimal word proliferation in formal languages.

scholarly journals A Formal Language to Convey Linguistic Information. A Study in Practical Logic

2002 ◽  
Vol 40 (4) ◽  
pp. 614-617
Author(s):  
Leonid L. Tsinman
Keyword(s):  
Machine Translation ◽  
Formal Language ◽  
Formal Languages ◽  
Linguistic Information ◽  
Computer Communication ◽  
Linguistic Data ◽  
Translation Systems ◽  
Linguistic Interfaces ◽  
Practical Logic

Abstract The author discusses problems of treating formal languages to present linguistic data in machine translation systems or linguistic interfaces for man-computer communication.

scholarly journals Characterization of completelyk-magic regular graphs

2017 ◽  
Vol 893 ◽  
pp. 012039
Author(s):  
A A Eniego ◽  
I J L Garces
Keyword(s):  
Regular Graphs

A characterization of bent functions in terms of strongly regular graphs

2001 ◽  
Vol 50 (9) ◽  
pp. 984-985 ◽  
Author(s):  
A. Bernasconi ◽  
B. Codenottl ◽  
J.M. Vanderkam
Keyword(s):  
Bent Functions ◽  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Strongly Regular

EXTENDED BACKUS-SYSTEMS FOR THE REPRESENTATION AND SPECIFICATION OF THE GENOME

2007 ◽  
Vol 05 (02b) ◽  
pp. 457-466 ◽  
Author(s):  
RALF HOFESTÄDT
Keyword(s):  
Formal Language ◽  
Formal Languages ◽  
Molecular Data ◽  
Adequate Representation ◽  
Theoretical Paper

In this theoretical paper, we focus to the usage of formal languages and define an extended Backus-System which will allow an adequate representation of molecular data. Furthermore, based on this new formalization we try to define the "complexity of organisms". Our results show that this formalization is useful for the syntactical specification of the genome interpreted as a formal language.

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