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Pushdown Automaton
In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines (see below). Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design. The term "pushdown" refers to the fact that the stack can be regarded as being "pushed down" like a tray dispenser at a cafeteria, since the operations never work on elements other than the top element. A stack automaton, by contrast, does allow access to and operations on deeper elements. Stack automata can recognize a strictly larger set of languages than pushdown automata. A nested stack automaton allows full access, and also allows stacked values to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Theory Of Computation
In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: ''"What are the fundamental capabilities and limitations of computers?".'' In order to perform a rigorous study of computation, computer scientists work with a mathematical abstraction of computers called a model of computation. There are several models in use, but the most commonly examined is the Turing machine. Computer scientists study the Turing machine because it is simple to formulate, can be analyzed and used to prove results, and because it represents what many consider the most powerful possible "reasonable" m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Linear Bounded Automaton
In computer science, a linear bounded automaton (plural linear bounded automata, abbreviated LBA) is a restricted form of Turing machine. Operation A linear bounded automaton is a Turing machine that satisfies the following three conditions: * Its input alphabet includes two special symbols, serving as left and right endmarkers. * Its transitions may not print other symbols over the endmarkers. * Its transitions may neither move to the left of the left endmarker nor to the right of the right endmarker. In other words: instead of having potentially infinite tape on which to compute, computation is restricted to the portion of the tape containing the input plus the two tape squares holding the endmarkers. An alternative, less restrictive definition is as follows: * Like a Turing machine, an LBA possesses a tape made up of cells that can contain symbols from a finite alphabet, a head that can read from or write to one cell on the tape at a time and can be moved, and a finite num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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General Recursive Function
In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the functions of lambda calculus and the functions tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Regular 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 Regular expression#Patterns for non-regular languages, 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 regular grammar, Type-3 grammars. Formal definition The collection of regular languages over an Alphabet (formal languages), alphabet Σ is defined recursively as follows: * The empty language ∅ is a regular language. * For each ''a'' ∈ Σ (''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Palindrome
A palindrome (Help:IPA/English, /ˈpæl.ɪn.droʊm/) is a word, palindromic number, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as ''madam'' or ''racecar'', the date "Twosday, 02/02/2020" and the sentence: "A man, a plan, a canal – Panama". The 19-letter Finnish language, Finnish word ''saippuakivikauppias'' (a soapstone vendor) is the longest single-word palindrome in everyday use, while the 12-letter term ''tattarrattat'' (from James Joyce in ''Ulysses (novel), Ulysses'') is the longest in English. The word ''palindrome'' was introduced by English poet and writer Henry Peacham (born 1578), Henry Peacham in 1638.Henry Peacham, ''The Truth of our Times Revealed out of One Mans Experience'', 1638p. 123 The concept of a palindrome can be dated to the 3rd-century BCE, although no examples survive. The earliest known examples are the 1st-century CE Latin acrostic word square, the Sator Square (which contains both word and senten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Greibach Normal Form
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 non-terminals. A non-strict form allows one exception to this format restriction for allowing the empty word (epsilon, ε) to be a member of the described language. The normal form was established by Sheila Greibach and it bears her name. More precisely, a context-free grammar is in Greibach normal form, if all production rules are of the form: :A \to a A_1 A_2 \cdots A_n where A is a nonterminal symbol, a is a terminal symbol, and A_1 A_2 \ldots A_n is a (possibly empty) sequence of nonterminal symbols. Observe that the grammar does not have left recursions. Every context-free grammar can be transformed into an equivalent grammar in Greibach normal form. Various constructions exist. Some do not permit the second form of rule and cannot transform context-free grammars that can generate the emp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Context-free Grammar
In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form : A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of terminals and/or nonterminals (\alpha can be empty). Regardless of which symbols surround it, the single nonterminal A on the left hand side can always be replaced by \alpha on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form \alpha A \beta \rightarrow \alpha \gamma \beta with A a nonterminal symbol and \alpha, \beta, and \gamma strings of terminal and/or nonterminal symbols. A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture, : \lan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Transitive Closure
In mathematics, the transitive closure of a homogeneous binary relation on a set (mathematics), set is the smallest Relation (mathematics), relation on that contains and is Transitive relation, transitive. For finite sets, "smallest" can be taken in its usual sense, of having the fewest related pairs; for infinite sets is the unique minimal element, minimal transitive superset of . For example, if is a set of airports and means "there is a direct flight from airport to airport " (for and in ), then the transitive closure of on is the relation such that means "it is possible to fly from to in one or more flights". More formally, the transitive closure of a binary relation on a set is the smallest (w.r.t. ⊆) transitive relation on such that ⊆ ; see . We have = if, and only if, itself is transitive. Conversely, transitive reduction adduces a minimal relation from a given relation such that they have the same closure, that is, ; however, many differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Reflexive Closure
In mathematics, the reflexive closure of a binary relation R on a set X is the smallest reflexive relation on X that contains R, i.e. the set R \cup \. For example, if X is a set of distinct numbers and x R y means "x is less than y", then the reflexive closure of R is the relation "x is less than or equal Definition The reflexive closure S of a relation R on a set X is given by S = R \cup \ In plain English, the reflexive closure of R is the union of R with the identity relation In mathematics, a homogeneous relation (also called endorelation) on a set ''X'' is a binary relation between ''X'' and itself, i.e. it is a subset of the Cartesian product . This is commonly phrased as "a relation on ''X''" or "a (binary) relation ... on X. Example As an example, if X = \ R = \ then the relation R is already reflexive by itself, so it does not differ from its reflexive closure. However, if any of the reflexive pairs in R was absent, it would be inserted for the reflexive closure. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |