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Splicing Rule
In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology. A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages. Definition Let ''A'' be an alphabet and ''L'' a language, that is, a subset of the free monoid ''A''∗. A splicing rule is a quadruple ''r'' = (''a'',''b'',''c'',''d'') of elements of ''A''∗, and the action of the rule ''r'' on ''L'' is to produce the language : r(L) = \ \ . If ''R'' is a set of rules then ''R''(''L'') is the union of the languages produced by the rules of ''R''. We say that ''R'' ''respects'' ''L'' if ''R''(''L'') is a subset of ''L''. The ''R''-closure of ''L'' is the union of ''L'' and all iterates of ''R'' on ''L'': clearly it is respected by ''R''. A splicing language is the ''R''-closure of a finite language.Anderson (2006) p.&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gene Splicing
Recombinant DNA (rDNA) molecules are DNA molecules formed by laboratory methods of genetic recombination (such as molecular cloning) that bring together genetic material from multiple sources, creating sequences that would not otherwise be found in the genome. Recombinant DNA is the general name for a piece of DNA that has been created by combining at least two fragments from two different sources. Recombinant DNA is possible because DNA molecules from all organisms share the same chemical structure, and differ only in the nucleotide sequence within that identical overall structure. Recombinant DNA molecules are sometimes called chimeric DNA, because they can be made of material from two different species, like the mythical chimera. R-DNA technology uses palindromic sequences and leads to the production of sticky and blunt ends. The DNA sequences used in the construction of recombinant DNA molecules can originate from any species. For example, plant DNA may be joined to bact ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Biology
Molecular biology is the branch of biology that seeks to understand the molecular basis of biological activity in and between cells, including biomolecular synthesis, modification, mechanisms, and interactions. The study of chemical and physical structure of biological macromolecules is known as molecular biology. Molecular biology was first described as an approach focused on the underpinnings of biological phenomena - uncovering the structures of biological molecules as well as their interactions, and how these interactions explain observations of classical biology. In 1945 the term molecular biology was used by physicist William Astbury. In 1953 Francis Crick, James Watson, Rosalind Franklin, and colleagues, working at Medical Research Council unit, Cavendish laboratory, Cambridge (now the MRC Laboratory of Molecular Biology), made a double helix model of DNA which changed the entire research scenario. They proposed the DNA structure based on previous research done by Ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Language
In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expressions engines, which are augmented with features that allow recognition of non-regular languages). Alternatively, a regular language can be defined as a language recognized by a finite automaton. The equivalence of regular expressions and finite automata is known as Kleene's theorem (after American mathematician Stephen Cole Kleene). In the Chomsky hierarchy, regular languages are the languages generated by Type-3 grammars. Formal definition The collection of regular languages over an alphabet Σ is defined recursively as follows: * The empty language Ø is a regular language. * For each ''a'' ∈ Σ (''a'' belongs to Σ), the singleton language is a regular language. * If ''A'' is a regular language, ''A''* ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syntactic Monoid
In mathematics and computer science, the syntactic monoid M(L) of a formal language L is the smallest monoid that recognizes the language L. Syntactic quotient The free monoid on a given set is the monoid whose elements are all the strings of zero or more elements from that set, with string concatenation as the monoid operation and the empty string as the identity element. Given a subset S of a free monoid M, one may define sets that consist of formal left or right inverses of elements in S. These are called quotients, and one may define right or left quotients, depending on which side one is concatenating. Thus, the right quotient of S by an element m from M is the set :S \ / \ m=\. Similarly, the left quotient is :m \setminus S=\. Syntactic equivalence The syntactic quotient induces an equivalence relation on M, called the syntactic relation, or syntactic equivalence (induced by S). The ''right syntactic equivalence'' is the equivalence relation :s \sim_S t \ \Leftrighta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semigroup Theory
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation of a semigroup is most often denoted multiplicatively: ''x''·''y'', or simply ''xy'', denotes the result of applying the semigroup operation to the ordered pair . Associativity is formally expressed as that for all ''x'', ''y'' and ''z'' in the semigroup. Semigroups may be considered a special case of magmas, where the operation is associative, or as a generalization of groups, without requiring the existence of an identity element or inverses. The closure axiom is implied by the definition of a binary operation on a set. Some authors thus omit it and specify three axioms for a group and only one axiom (associativity) for a semigroup. As in the case of groups or magmas, the semigroup operation need not be commutative, so ''x''·''y'' is not necessarily equal to ''y''·''x''; a well-known example of an operation that is ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Languages
In logic, mathematics, computer science, and linguistics, a formal language consists of string (computer science), words whose symbol (formal), letters are taken from an alphabet (formal languages), alphabet and are well-formedness, well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
