Formal languageIn logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet". The alphabet of a formal language consists of symbols that concatenate into strings (also called "words"). Words that belong to a particular formal language are sometimes called well-formed words. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar.
String (computer science)In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding.
Symbol (formal)A formal symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.
Finite setIn mathematics, a finite set is a collection of finitely many different things; the things are called elements or members of the set and are typically mathematical objects, such as numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. Informally, a finite set is a set which one could in principle count and finish counting. For example, { 2 , 4 , 6 , 8 , 10 } {\displaystyle \{2,4,6,8,10\}} is a finite set with five elements.
Terminal and nonterminal symbolsIn formal languages, terminal and nonterminal symbols are parts of the vocabulary under a formal grammar. Vocabulary is a finite, nonempty set of symbols. Terminal symbols are symbols that cannot be replaced by other symbols of the vocabulary. Nonterminal symbols are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar. A formal grammar defines a formal language over the vocabulary of the grammar.
SequenceIn mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members (also called elements, or terms). Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.
CardinalityIn mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets. That is, if their objects can be paired such that each object has a pair, and no object is paired more than once. Two sets are said to be equinumerous or have the same cardinality if there exists a one-to-one correspondence between them.
Character (computing)In computing and telecommunications, a character is the encoded representation of a natural language character (including letter, numeral and punctuation), whitespace (space or tab), or a control character (controls computer hardware that consumes character-based data). A sequence of characters is called a string. Some character encoding systems represent each character using a fixed number of bits whereas other systems use varying sizes.
GlyphPurposeful written mark Various glyphs representing lower case letter ⟨a⟩ in various typefaces and as single- and double-storey; they are allographs of the same grapheme A glyph (/ɡlɪf/ GLIF) is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface (or computer font), of an element of written language.
Uncountable setInfinite set that is not countable In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers.Countable setA mathematical set is countable if either it is finite or it can be put in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements.
PhonemeBasic unit of phonology A phoneme (/ˈfoʊniːm/ FOH-neem) is a set of similar speech sounds that are perceptually regarded by the speakers of a language as a single basic sound—the smallest possible phonetic unit—that helps distinguish one word from another. All languages contain phonemes (or the spatial–gestural equivalent in sign languages), and all spoken languages include both consonant and vowel phonemes.*As an Amazon Associate I earn from qualifying purchases.