Formal language theory in the context of "Context-free grammar"

Formal epistemology uses formal methods from decision theory, logic, probability theory and computability theory to model and reason about issues of epistemological interest. Work in this area spans several academic fields, including philosophy, computer science, economics, and statistics. The focus of formal epistemology has tended to differ somewhat from that of traditional epistemology, with topics like uncertainty, induction, and belief revision garnering more attention than the analysis of knowledge, skepticism, and issues with justification. Formal epistemology extenuates into formal language theory.

In theoretical computer science and formal language theory, a regular grammar is a grammar that is right-regular or left-regular.While their exact definition varies from textbook to textbook, they all require that

• all production rules have at most one non-terminal symbol;
• that symbol is either always at the end or always at the start of the rule's right-hand side.

Every regular grammar describes a regular language.

In formal language theory, an alphabet, often called a vocabulary in the context of terminal and nonterminal symbols, is a non-empty set of indivisible symbols/characters/glyphs, typically thought of as representing letters, characters, digits, phonemes, or even words. The definition is used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and, depending on its purpose, may be finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., ${\displaystyle \{v_{1},v_{2},\ldots \}}$), or even uncountable (e.g., ${\displaystyle \{v_{x}:x\in \mathbb {R} \}}$).

Strings, also known as "words" or "sentences", over an alphabet are defined as a sequence of the symbols from the alphabet set. For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is {0,1}, the binary alphabet, and "00101111" is an example of a binary string. Infinite sequences of symbols may be considered as well (see Omega 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 expression engines, which are augmented with features that allow the recognition of non-regular languages).

Alternatively, a regular language can be defined as a language recognised 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.

In formal language theory, the empty string, also known as the empty word or null string, is the unique string of length zero.