|
Wirth–Weber Precedence Relationship
In computer science, a ''Wirth–Weber relationship'' between a pair of symbols (V_t \cup V_n) is necessary to determine if a formal grammar is a simple precedence grammar. In such a case, the simple precedence parser can be used. The relationship is named after computer scientists Niklaus Wirth Niklaus Emil Wirth (born 15 February 1934) is a Swiss computer scientist. He has designed several programming languages, including Pascal (programming language), Pascal, and pioneered several classic topics in software engineering. In 1984, he w ... and Helmut Weber. The goal is to identify when the viable prefixes have the ''pivot'' and must be reduced. A \gtrdot means that the ''pivot'' is found, a \lessdot means that a potential ''pivot'' is starting, and a \doteq means that a relationship remains in the same ''pivot''. Formal definition : G = \langle V_n, V_t, S, P \rangle :: \begin X \doteq Y &\iff \begin A \to \alpha X Y \beta \in P \\ A \in V_n \\ \alpha , \beta \in (V_n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammar
In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) describes how to form strings from a language's alphabet that are valid according to the language's syntax. A grammar does not describe the meaning of the strings or what can be done with them in whatever context—only their form. A formal grammar is defined as a set of production rules for such strings in a formal language. Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a "recognizer"—a function in computing that deter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Precedence Grammar
A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser. The concept was first created in 1964 by Claude Pair, and was later rediscovered, from ideas due to Robert Floyd, by Niklaus Wirth and Helmut Weber who published a paper, entitled ''EULER: a generalization of ALGOL, and its formal definition'', published in 1966 in the Communications of the ACM. Formal definition G = (''N'', Σ, ''P'', ''S'') is a simple precedence grammar if all the production rules in ''P'' comply with the following constraints: * There are no erasing rules (ε-productions) * There are no useless rules In formal language theory, a context-free grammar (CFG) is a formal grammar whose Production (computer science), production rules are of the form :A\ \to\ \alpha with A a ''single'' nonterminal symbol, and \alpha a string of Terminal and nonter ... (unreachable symbols or unproductive rules) * For each pair of symbols ''X'', ''Y'' (''X'', ''Y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Precedence Parser
In computer science, a simple precedence parser is a type of bottom-up parser for context-free grammars that can be used only by simple precedence grammars. The implementation of the parser is quite similar to the generic bottom-up parser. A stack is used to store a viable prefix of a sentential form from a rightmost derivation. The symbols ⋖, ≐ and ⋗ are used to identify the pivot, and to know when to Shift or when to Reduce. Implementation * Compute the Wirth–Weber precedence relationship table for a grammar with initial symbol S. * Initialize a stack with the starting marker $. * Append an ending marker $ to the string being parsed (Input). * Until Stack equals "$ S" and Input equals "$" ** Search the table for the relationship between Top(stack) and NextToken(Input) ** if the relationship is ⋖ or ≐ *** Shift: *** Push(Stack, relationship) *** Push(Stack, NextToken(Input)) *** RemoveNextToken(Input) ** if the relationship is ⋗ *** Reduce: *** SearchProductionToRe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niklaus Wirth
Niklaus Emil Wirth (born 15 February 1934) is a Swiss computer scientist. He has designed several programming languages, including Pascal (programming language), Pascal, and pioneered several classic topics in software engineering. In 1984, he won the Turing Award, generally recognized as the highest distinction in computer science, for developing a sequence of innovative computer languages. Biography Wirth was born in Winterthur, Switzerland, in 1934. In 1959, he earned a Bachelor of Science (B.S.) degree in electronic engineering from the Swiss Federal Institute of Technology Zürich (ETH Zürich). In 1960, he earned a Master of Science (MSc) from Université Laval, Canada. Then in 1963, he was awarded a PhD in Electrical Engineering and Computer Science (EECS) from the University of California, Berkeley, supervised by the computer design pioneer Harry Huskey. From 1963 to 1967, he served as assistant professor of computer science at Stanford University and again at the Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LL Parser
In computer science, an LL parser (Left-to-right, leftmost derivation) is a top-down parser for a restricted context-free language. It parses the input from Left to right, performing Leftmost derivation of the sentence. An LL parser is called an LL(''k'') parser if it uses ''k'' tokens of lookahead when parsing a sentence. A grammar is called an LL(''k'') grammar if an LL(''k'') parser can be constructed from it. A formal language is called an LL(''k'') language if it has an LL(''k'') grammar. The set of LL(''k'') languages is properly contained in that of LL(''k''+1) languages, for each ''k'' ≥ 0. A corollary of this is that not all context-free languages can be recognized by an LL(''k'') parser. An LL parser is called LL-regular (LLR) if it parses an LL-regular language. The class of LLR grammars contains every LL(k) grammar for every k. For every LLR grammar there exists an LLR parser that parses the grammar in linear time. Two nomenclative outlier parser typ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Product
In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\times B = \. A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product is taken, the cells of the table contain ordered pairs of the form . One can similarly define the Cartesian product of ''n'' sets, also known as an ''n''-fold Cartesian product, which can be represented by an ''n''-dimensional array, where each element is an ''n''-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product. Examples A deck of cards An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
