"A regular language (also called a rational language)..."
Regular languages are a type of language that can be recognized by a deterministic finite automaton (DFA) or a non-deterministic finite automaton (NFA).
Alphabet: Set of symbols that are used to form words in the language.
String: A sequence of symbols from the alphabet.
Language: A set of strings from the alphabet.
Regular Expressions: A notation to describe regular languages.
Regular grammar: A set of productions to generate strings in a regular language.
Finite automata: A machine that can recognize a regular language.
Deterministic finite automata (DFA): A finite automaton with a unique transition for each input symbol.
Non-deterministic finite automata (NFA): A finite automaton that can transition to multiple states for a single input symbol.
Equivalence of DFA and NFA: Theorems that prove there is no difference in the languages recognized by a DFA or an NFA.
Regular language operations: Union, concatenation, and Kleene closure of regular languages.
Pumping lemma: A tool to prove a language is not regular.
Myhill-Nerode theorem: A tool to determine if a language is regular.
Minimization of finite automata: Technique to reduce the number of states in a DFA.
Simulating a DFA in a programming language: Implementation of a DFA in a programming language.
Applications of regular languages: Regular expressions are used in text processing, compilers, and database searching.
Regular expressions: Regular expressions are a concise way to represent a pattern to match strings. They consist of a series of symbols representing the alphabet and operators that modify the pattern.
Regular grammars: Regular grammars are a type of context-free grammar that generates regular languages. A regular grammar has productions of the form A -> aB or A -> a, where A and B are nonterminals and a is a terminal symbol.
Finite automata: Finite automata are machines that accept or reject input strings based on a set of rules. There are two types of finite automata: deterministic finite automata (DFA) and non-deterministic finite automata (NFA).
Regular expressions to finite automata: Regular expressions can be easily converted into finite automata. This means that any regular language can be generated by a regular expression or recognized by a finite automaton.
Regular expressions to regular grammars: Regular expressions can also be converted into regular grammars. This means that any regular language can be generated by a regular expression or recognized by a regular grammar.
Regular expressions to regular expressions: Regular expressions can be simplified using various algebraic laws. This process is known as regular expression simplification or reduction.
"A regular language can be defined by a regular expression..."
"...in the strict sense in theoretical computer science..."
"...features that allow the 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)."
"...regular languages are the languages generated by Type-3 grammars." The remaining questions require paraphrasing of the paragraph:
Theoretical computer science and formal language theory focus on the study of regular languages.
Regular expressions can recognize formal languages that can be defined as regular languages.
The strict sense of regular expressions in theoretical computer science does not include features for recognizing non-regular languages, which modern regular expression engines possess.
A regular language is defined by a regular expression, providing a formal representation of the language.
A finite automaton is a computational model that recognizes regular languages.
Kleene's theorem establishes the equivalence between regular expressions and finite automata.
Regular languages are classified as the languages generated by Type-3 grammars in the Chomsky hierarchy.
The Chomsky hierarchy provides a classification of formal grammars and languages according to their generative power.
Regular languages are lower in the hierarchy compared to other types of languages.
Modern regular expression engines include additional features that extend their capabilities beyond recognizing regular languages.
Examples of non-regular languages are languages that contain nested structures or require memory to recognize.
Regular languages serve as a foundation in formal language theory and provide a starting point for studying more complex language classes.