Enhance Your Learning with Automata Theory Flash Cards for quick learning
A branch of computer science that deals with the study of abstract machines and computational models, including finite automata, regular expressions, context-free grammars, and Turing machines.
A mathematical model of computation that consists of a finite set of states, an input alphabet, a transition function, a start state, and a set of accepting states.
A sequence of characters that defines a search pattern, used for matching strings in formal language theory and text processing.
A formal grammar in which production rules are of the form A -> α, where A is a nonterminal symbol and α is a string of terminals and/or nonterminals.
A type of automaton that extends the capabilities of a finite automaton by adding a stack, allowing it to recognize context-free languages.
A theoretical computing device that can simulate the logic of any computer algorithm, using an infinite tape divided into cells and a read-write head.
The property of a language or problem being solvable by an algorithm, where the algorithm always terminates and produces the correct output.
The property of a language or problem being unsolvable by an algorithm, where no algorithm can determine whether a given input belongs to the language or problem.
The study of what can and cannot be computed by various computational models, including Turing machines and other abstract machines.
A set of strings over a given alphabet, defined by a formal grammar or automaton, used in the study of formal languages and automata theory.
A formal language that can be described by a regular expression or recognized by a finite automaton.
A formal language that can be described by a context-free grammar or recognized by a pushdown automaton.
A classification of formal grammars and languages into four levels, based on their generative power and the types of formal languages they can describe.
A tool used in the theory of formal languages to prove that certain languages are not context-free or not regular.
The problem of determining, given a description of a program and an input, whether the program will eventually halt or run forever.
A Turing machine that can simulate the logic of any other Turing machine, used to define the concept of computability.
The hypothesis that any function that can be computed by an algorithm can be computed by a Turing machine, or equivalently, by any other computational model.
An operation that can be performed on regular languages, such as union, concatenation, and Kleene star.
An operation that can be performed on context-free languages, such as union, concatenation, and Kleene star.
A lemma used to prove that a language is not regular by showing that it cannot satisfy the pumping property.
A lemma used to prove that a language is not context-free by showing that it cannot satisfy the pumping property.
A type of finite automaton where multiple transitions may be possible for a given input symbol and current state.
A type of finite automaton where there is exactly one transition for each input symbol and current state.
A type of formal grammar where all production rules are of the form A -> aB or A -> ε, where A and B are nonterminal symbols and a is a terminal symbol.
A type of formal grammar where production rules are of the form α -> β, where α and β are strings of terminals and/or nonterminals, and the length of α is less than or equal to the length of β.
A type of formal grammar where production rules are of the form α -> β, where α and β are strings of terminals and/or nonterminals, and there are no restrictions on the lengths of α and β.
A set of strings that can be described by a regular expression or recognized by a finite automaton.
A set of strings that can be described by a context-free grammar or recognized by a pushdown automaton.
A set of strings that can be described by a context-sensitive grammar or recognized by a linear-bounded automaton.
A set of strings that can be recognized by a Turing machine, where the machine may not halt for strings not in the set.
A language for which there exists an algorithm that can determine, for any given input, whether the input belongs to the language or not.
A language for which no algorithm can determine, for any given input, whether the input belongs to the language or not.
The set of descriptions of Turing machines that halt on a given input.
The set of descriptions of Turing machines that accept a given input.
A set of symbols, axioms, and rules for deriving new symbols, used in the study of formal languages and formal proofs.
A sequence of statements, each of which is either an axiom or follows from previous statements using the rules of inference, used to establish the truth of a statement in a formal system.
A set of rules for deriving formal proofs in a formal system, including axioms, rules of inference, and rules for manipulating symbols.
The study of formal systems, formal proofs, and their properties, including consistency, completeness, and soundness.
A branch of mathematics and philosophy that studies formal systems, formal proofs, and their applications in reasoning and computation.
A branch of computer science and linguistics that studies formal languages, formal grammars, and their applications in computation and communication.
A branch of linguistics and computer science that studies the meaning of programming languages and natural languages using formal methods.
A process of proving or disproving the correctness of a system or program using formal methods, such as formal proofs or model checking.
A set of techniques and tools for specifying, designing, and verifying software and hardware systems using formal languages, formal proofs, and formal models.
A precise description of the behavior and properties of a system or program using a formal language, used in formal methods and formal verification.
A mathematical or logical representation of a system or program, used in formal methods and formal verification to reason about its behavior and properties.
A software tool or system that processes formal languages, such as compilers, interpreters, and parsers.
The process of determining whether a given string belongs to a formal language, using automata, grammars, or other formal models.
The process of generating strings that belong to a formal language, using automata, grammars, or other formal models.
The study of the computational complexity of formal languages, including time complexity, space complexity, and other measures of complexity.
The study of the equivalence of formal languages, including language containment, language equality, and other notions of language equivalence.
The study of operations that can be performed on formal languages, such as union, intersection, concatenation, and Kleene star.
The study of closure properties of formal languages, including closure under union, intersection, concatenation, Kleene star, and other operations.
A lemma used to prove that a language is not regular or not context-free by showing that it cannot satisfy the pumping property.
A problem of determining, for a given formal language, whether a given string belongs to the language or not.
A problem of determining, for a given formal language and string, whether the string belongs to the language or not.
A problem of determining, for two given formal languages, whether the languages are equivalent or not.
A problem of determining, for two given formal languages, whether one language is contained in the other or not.
A problem of determining, for two given formal languages, whether the intersection of the languages is empty or not.
A problem of determining, for two given formal languages, whether the concatenation of the languages contains a given string or not.
A problem of determining, for a given formal language and string, whether the string can be obtained by concatenating zero or more strings from the language.