Non-Repetitive 3-Coloring of Subdivided Graphs

Let W be a finite language and let Wc be the closure of W under taking subwords. Let S(W) denote the Rees quotient of a free monoid over the ideal consisting of all words that are not in Wc. We call W finitely based if the monoid S(W) is finitely based. Although these semigroups have easy structure they behave "generically" with respect to the finite basis property [6]. In this paper, we describe all finitely based words in a two-letter alphabet. We also find some necessary and some sufficient conditions for a set of words to be finitely based.

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Autonomous assembly of synthetic oligonucleotides built from an expanded DNA alphabet. Total synthesis of a gene encoding kanamycin resistance

Beilstein Journal of Organic Chemistry ◽

10.3762/bjoc.10.245 ◽

2014 ◽

Vol 10 ◽

pp. 2348-2360 ◽

Cited By ~ 13

Author(s):

Kristen K Merritt ◽

Kevin M Bradley ◽

Daniel Hutter ◽

Mariko F Matsuura ◽

Diane J Rowold ◽

...

Keyword(s):

Solid Phase ◽

Pcr Amplification ◽

Kanamycin Resistance ◽

Dna Fragments ◽

Gene Encoding ◽

Synthetic Dna ◽

Information Density ◽

Letter Alphabet ◽

New Strategy ◽

Autonomous Assembly

Background: Many synthetic biologists seek to increase the degree of autonomy in the assembly of long DNA (L-DNA) constructs from short synthetic DNA fragments, which are today quite inexpensive because of automated solid-phase synthesis. However, the low information density of DNA built from just four nucleotide “letters”, the presence of strong (G:C) and weak (A:T) nucleobase pairs, the non-canonical folded structures that compete with Watson–Crick pairing, and other features intrinsic to natural DNA, generally prevent the autonomous assembly of short single-stranded oligonucleotides greater than a dozen or so. Results: We describe a new strategy to autonomously assemble L-DNA constructs from fragments of synthetic single-stranded DNA. This strategy uses an artificially expanded genetic information system (AEGIS) that adds nucleotides to the four (G, A, C, and T) found in standard DNA by shuffling hydrogen-bonding units on the nucleobases, all while retaining the overall Watson–Crick base-pairing geometry. The added information density allows larger numbers of synthetic fragments to self-assemble without off-target hybridization, hairpin formation, and non-canonical folding interactions. The AEGIS pairs are then converted into standard pairs to produce a fully natural L-DNA product. Here, we report the autonomous assembly of a gene encoding kanamycin resistance using this strategy. Synthetic fragments were built from a six-letter alphabet having two AEGIS components, 5-methyl-2’-deoxyisocytidine and 2’-deoxyisoguanosine (respectively S and B), at their overlapping ends. Gaps in the overlapped assembly were then filled in using DNA polymerases, and the nicks were sealed by ligase. The S:B pairs in the ligated construct were then converted to T:A pairs during PCR amplification. When cloned into a plasmid, the product was shown to make Escherichia coli resistant to kanamycin. A parallel study that attempted to assemble similarly sized genes with optimally designed standard nucleotides lacking AEGIS components gave successful assemblies of up to 16 fragments, but generally failed when larger autonomous assemblies were attempted. Conclusion: AEGIS nucleotides, by increasing the information density of DNA, allow larger numbers of DNA fragments to autonomously self-assemble into large DNA constructs. This technology can therefore increase the size of DNA constructs that might be used in synthetic biology.

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That 43 letter alphabet

Journal of the Reading Specialist ◽

10.1080/19388076309556847 ◽

1963 ◽

Vol 3 (1) ◽

pp. 9-12

Author(s):

Albert J. Mazurkiwicz

Keyword(s):

Letter Alphabet

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UNARY FA-PRESENTABLE SEMIGROUPS

International Journal of Algebra and Computation ◽

10.1142/s0218196712500385 ◽

2012 ◽

Vol 22 (04) ◽

pp. 1250038 ◽

Cited By ~ 1

Author(s):

ALAN J. CAIN ◽

NIK RUŠKUC ◽

RICHARD M. THOMAS

Keyword(s):

Difficult Problem ◽

Decision Problems ◽

Finite Model ◽

Locally Finite ◽

Letter Alphabet ◽

Significant Interest ◽

Automatic Presentations ◽

The Relationship ◽

Completely Simple

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult problem in general. A restricted problem, also of significant interest, is to ask this question for unary automatic presentations: automatic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally finite, but non-finitely generated unary FA-presentable semigroups may be infinite. Every unary FA-presentable semigroup satisfies some Burnside identity. We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classification is given of the unary FA-presentable completely simple semigroups.

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Unambiguous Conjunctive Grammars over a One-Letter Alphabet

Developments in Language Theory - Lecture Notes in Computer Science ◽

10.1007/978-3-642-38771-5_25 ◽

2013 ◽

pp. 277-288 ◽

Cited By ~ 1

Author(s):

Artur Jeż ◽

Alexander Okhotin

Keyword(s):

Letter Alphabet ◽

Conjunctive Grammars

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Compound Poisson approximations for word patterns under Markovian hypotheses

Journal of Applied Probability ◽

10.1017/s0021900200103353 ◽

1995 ◽

Vol 32 (04) ◽

pp. 877-892 ◽

Cited By ~ 4

Author(s):

Mark X. Geske ◽

Anant P. Godbole ◽

Andrew A. Schaffner ◽

Allison M. Skolnick ◽

Garrick L. Wallstrom

Keyword(s):

Markov Chain ◽

State Space ◽

Compound Poisson ◽

Letter Word ◽

Stationary Markov Chain ◽

Letter Alphabet ◽

Poisson Approximations

Consider a stationary Markov chainwith state space consisting of theξ-letter alphabet set Λ= {a1, a2, ···,aξ}.We study the variablesM=M(n, k) andN=N(n, k),defined, respectively, as the number of overlapping and non-overlapping occurrences of a fixed periodick-letter word, and use the Stein–Chen method to obtain compound Poisson approximations for their distribution.

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A CHARACTERIZATION OF RECOGNIZABLE PICTURE LANGUAGES

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001494000255 ◽

1994 ◽

Vol 08 (02) ◽

pp. 501-508 ◽

Cited By ~ 2

Author(s):

KATSUSHI INOUE ◽

ITSUO TAKANAMI

Keyword(s):

Finite Automata ◽

Two Dimensional ◽

Open Problems ◽

Nondeterministic Finite Automata ◽

Letter Alphabet ◽

The Family ◽

On Line ◽

Picture Languages

This paper first shows that REC, the family of recognizable picture languages in Giammarresi and Restivo,3 is equal to the family of picture languages accepted by two-dimensional on-line tessellation acceptors in Inoue and Nakamura.5 By using this result, we then solve open problems in Giammarresi and Restivo,3 and show that (i) REC is not closed under complementation, and (ii) REC properly contains the family of picture languages accepted by two-dimensional nondeterministic finite automata even over a one letter alphabet.

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ON THE NUMBER OF ABELIAN BORDERED WORDS (WITH AN EXAMPLE OF AUTOMATIC THEOREM-PROVING)

International Journal of Foundations of Computer Science ◽

10.1142/s0129054114400267 ◽

2014 ◽

Vol 25 (08) ◽

pp. 1097-1110 ◽

Cited By ~ 3

Author(s):

DANIEL GOČ ◽

NARAD RAMPERSAD ◽

MICHEL RIGO ◽

PAVEL SALIMOV

Keyword(s):

Theorem Proving ◽

Triangular Lattice ◽

Automatic Theorem Proving ◽

Combinatorial Objects ◽

Letter Alphabet ◽

Automatic Sequences ◽

Motzkin Paths ◽

Automatic Theorem

In the literature, many bijections between (labeled) Motzkin paths and various other combinatorial objects are studied. We consider abelian (un)bordered words and show the connection with irreducible symmetric Motzkin paths and paths in ℤ not returning to the origin. This study can be extended to abelian unbordered words over an arbitrary alphabet and we derive expressions to compute the number of these words. In particular, over a 3-letter alphabet, the connection with paths in the triangular lattice is made. Finally, we characterize the lengths of the abelian unbordered factors occurring in the Thue–Morse word using some kind of automatic theorem-proving provided by a logical characterization of the k-automatic sequences.

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