Parsing Boolean grammars over a one-letter alphabet using online convolution

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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BOOLEAN GRAMMARS AND GSM MAPPINGS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054110007568 ◽

2010 ◽

Vol 21 (05) ◽

pp. 799-815 ◽

Cited By ~ 8

Author(s):

TOMMI LEHTINEN ◽

ALEXANDER OKHOTIN

Keyword(s):

Sequential Machine ◽

Language Family ◽

Conjunctive Grammars ◽

Boolean Grammars

It is proved that the language family generated by Boolean grammars is effectively closed under injective gsm mappings and inverse gsm mappings (where gsm stands for a generalized sequential machine). The same results hold for conjunctive grammars, unambiguous Boolean grammars and unambiguous conjunctive grammars.

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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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Non-Repetitive 3-Coloring of Subdivided Graphs

The Electronic Journal of Combinatorics ◽

10.37236/253 ◽

2009 ◽

Vol 16 (1) ◽

Cited By ~ 7

Author(s):

Andrzej Pezarski ◽

Michał Zmarz

Keyword(s):

Letter Alphabet

We show that every graph can be subdivided in a way that the resulting graph can be colored without repetitions on paths using only 3 colors. This extends the result of Thue asserting the existence of arbitrarily long nonrepetitive strings over a 3-letter alphabet.

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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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