In formal language theory, a context-sensitive language is a language that can be defined by a context-sensitive grammar. Context-sensitive is known as type-1 in the Chomsky hierarchy of formal languages.
A finite-state machine (FSM) or finite-state automaton, finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—deterministic finite-state machines and non-deterministic finite-state machines. For any non-deterministic finite-state machine, an equivalent deterministic one can be constructed.
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack.
In formal language theory, a context-free grammar is in Greibach normal form (GNF) if the right-hand sides of all production rules start with a terminal symbol, optionally followed by some variables. A non-strict form allows one exception to this format restriction for allowing the empty word to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name.
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science with close connections to mathematical logic. The word automata comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states and transitions. As the automaton sees a symbol of input, it makes a transition to another state, according to its transition function, which takes the previous state and current input symbol as its arguments.
In computer science, an ambiguous grammar is a context-free grammar for which there exists a string that can have more than one leftmost derivation or parse tree. Every non-empty context-free language admits an ambiguous grammar by introducing e.g. a duplicate rule. A language that only admits ambiguous grammars is called an inherently ambiguous language. Deterministic context-free grammars are always unambiguous, and are an important subclass of unambiguous grammars; there are non-deterministic unambiguous grammars, however.
In computer science, a linear grammar is a context-free grammar that has at most one nonterminal in the right-hand side of each of its productions.
In computer science, a linear bounded automaton is a restricted form of Turing machine.
In automata theory, a deterministic pushdown automaton is a variation of the pushdown automaton. The class of deterministic pushdown automata accepts the deterministic context-free languages, a proper subset of context-free languages.
Seymour Ginsburg was an American pioneer of automata theory, formal language theory, and database theory, in particular; and computer science, in general. His work was influential in distinguishing theoretical Computer Science from the disciplines of Mathematics and Electrical Engineering.
Indexed languages are a class of formal languages discovered by Alfred Aho; they are described by indexed grammars and can be recognized by nested stack automata.
In formal language theory, deterministic context-free languages (DCFL) are a proper subset of context-free languages. They are the context-free languages that can be accepted by a deterministic pushdown automaton. DCFLs are always unambiguous, meaning that they admit an unambiguous grammar. There are non-deterministic unambiguous CFLs, so DCFLs form a proper subset of unambiguous CFLs.
In computer science, in particular in the field of formal language theory, an abstract family of languages is an abstract mathematical notion generalizing characteristics common to the regular languages, the context-free languages and the recursively enumerable languages, and other families of formal languages studied in the scientific literature.
In formal language theory, a cone is a set of formal languages that has some desirable closure properties enjoyed by some well-known sets of languages, in particular by the families of regular languages, context-free languages and the recursively enumerable languages. The concept of a cone is a more abstract notion that subsumes all of these families. A similar notion is the faithful cone, having somewhat relaxed conditions. For example, the context-sensitive languages do not form a cone, but still have the required properties to form a faithful cone.
Rajeev Alur is an American professor of computer science at the University of Pennsylvania who has made contributions to formal methods, programming languages, and automata theory, including notably the introduction of timed automata and nested words.
An abstract family of acceptors (AFA) is a grouping of generalized acceptors. Informally, an acceptor is a device with a finite state control, a finite number of input symbols, and an internal store with a read and write function. Each acceptor has a start state and a set of accepting states. The device reads a sequence of symbols, transitioning from state to state for each input symbol. If the device ends in an accepting state, the device is said to accept the sequence of symbols. A family of acceptors is a set of acceptors with the same type of internal store. The study of AFA is part of AFL (abstract families of languages) theory.
In computer science, more specifically in automata and formal language theory, nested words are a concept proposed by Alur and Madhusudan as a joint generalization of words, as traditionally used for modelling linearly ordered structures, and of ordered unranked trees, as traditionally used for modelling hierarchical structures. Finite-state acceptors for nested words, so-called nested word automata, then give a more expressive generalization of finite automata on words. The linear encodings of languages accepted by finite nested word automata gives the class of visibly pushdown languages. The latter language class lies properly between the regular languages and the deterministic context-free languages. Since their introduction in 2004, these concepts have triggered much research in that area.
JFLAP is interactive educational software written in Java for experimenting with topics in the computer science area of formal languages and automata theory, primarily intended for use at the undergraduate level or as an advanced topic for high school. JFLAP allows one to create and simulate structures, such as programming a finite state machine, and experiment with proofs, such as converting a nondeterministic finite automaton (NFA) to a deterministic finite automaton (DFA).
Michael A. Harrison is a computer scientist, in particular a pioneer in the area of formal languages.
