"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."
Study of formal grammar, syntax, and semantics of computer languages, including Chomsky hierarchy, context-free languages, and pushdown automata.
Regular languages: This topic involves the study of languages that can be recognized by regular expressions or finite state automata. It includes understanding the concept of regular expressions, regular sets, closure properties, pumping lemma, and non-regular languages.
Context-free languages: This topic focuses on languages that can be generated by context-free grammars. It involves understanding the concept of context-free grammars, pushdown automata, closure properties, and parsing techniques like the CYK algorithm.
Turing machines: This topic covers the concept of Turing machines and their computational power. It includes understanding the concept of deterministic and non-deterministic Turing machines, universal Turing machines, and the Church-Turing thesis.
Undecidability: This topic involves understanding the concept of undecidable problems and their relationship with Turing machines. It includes understanding the halting problem, Rice's theorem, and the concept of reducibility.
Complexity theory: This topic covers the study of the complexity of algorithms and problems. It includes understanding the concept of time and space complexity, the classes P, NP, NP-complete, and NP-hard, and the polynomial-time hierarchy.
Formal language theory: This topic involves studying the mathematical properties of formal languages. It includes understanding the concept of Chomsky hierarchy, regular and context-free languages, and the relationship between language classes.
Computability theory: This topic involves understanding the limits of computation. It includes understanding the concept of recursive and recursively enumerable languages, Church-Turing thesis, and the concept of decidable and undecidable problems.
Grammars: This topic covers the study of different types of grammars, including regular, context-free, and context-sensitive grammars. It includes understanding the generative power of these grammars and their relationship with language classes.
Finite-state machines: This topic covers the study of finite-state machines and their computational power. It includes understanding the concept of deterministic and non-deterministic finite automata, and Mealy and Moore machines.
Mathematical logic: This topic covers the study of mathematical logic and its relationship with formal language theory. It includes understanding the concepts of propositional and predicate logic, truth tables, and logical reasoning.
Regular language: A language is called regular if it can be generated by a regular expression or a finite automaton. This is the most basic type of formal language.
Context-free language: A language is called context-free if it can be generated by a context-free grammar. These languages are used in programming languages, compilers, and operating systems.
Context-sensitive language: A language is called context-sensitive if it can be generated by a context-sensitive grammar. These languages are used in natural language processing, artificial intelligence, and robotics.
Recursive language: A language is called recursive if it is recognized by a Turing machine. These languages are used in algorithms and automata theory.
Recursively enumerable language: A language is called recursively enumerable if it is generated by a Turing machine. These languages are used in cryptography, communication, and computation.
Deterministic Context-free Language (DCFL): A context-free language is DCFL when a pushdown annotator could operate like a DFA (Deterministic Finite Automata).
Deterministic Context-sensitive Language (DCSL): Context-sensitive language is DCSL when a linear-bounded non-deterministic Turing machine can be transformed into a Deterministic Turing machine, then we say it is DCSL.
Unrestricted Grammar Language: A language is unrestricted if it can be generated by an unrestricted grammar. This is the most powerful and expressive type of formal language, but it is rarely used in practical applications.
Type-0 Language: Type-0 languages are Turing-recognizable languages.
Type-1 Language: Type-1 Languages are context-sensitive languages.
Type-2 Language: Type-2 Languages are context-free languages.
Type-3 Language: Type-3 Languages are regular languages.
"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..."
"...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..."
"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 computational complexity theory, decision problems are typically defined as formal languages..."
"...and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power."
"In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems..."
"Mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way."
"The field of formal language theory studies primarily the purely syntactical aspects of such languages..."
"Formal language theory sprang out of linguistics..."
"...as a way of understanding the syntactic regularities of natural languages."
"In logic, mathematics, computer science, and linguistics..."
"A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar..."
"...decision problems are typically defined as formal languages..."
"Mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way."
"Formal languages are used to represent the syntax of axiomatic systems..."
"The field of formal language theory studies primarily the purely syntactical aspects of such languages..."
"Formal language theory sprang out of linguistics..."