Compiler Design and Construction (CSC 352) by Bhupendra Singh Saud for B
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Formal Language (3B)
Formal Language (3B) ● Context Free Language Young Won Lim 6/9/18 Copyright (c) 2018 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to [email protected]. This document was produced by using LibreOffice and Octave. Young Won Lim 6/9/18 Regular Language a regular language (a rational language) is a formal language that can be expressed using a regular expression, in the strict sense 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. Regular languages are very useful in input parsing and programming language design. https://en.wikipedia.org/wiki/Regular_language Young Won Lim Context Free Language (3B) 3 6/9/18 Regular Language – Formal Definition The collection of regular languages over an alphabet Σ is defined recursively as follows: The empty language Ø, and the empty string language {ε} are regular languages. For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. If A and B are regular languages, then A ∪ B (union), A • B (concatenation), and A* (Kleene star) are regular languages. No other languages over Σ are regular. -
Regular Expressions: Basic Notions
Regular expressions: Basic notions Fritz Henglein Department of Computer Science University of Copenhagen Email: [email protected] 2nd International Summer School on Advances in Programming Languages Edinburgh, Scotland 2014-08-22 Kleene Meets Church (KMC) Research project on type theory for proof-theoretic foundations of formal language theory, specifically regular languages; semantically well-behaved, powerful, scalable, efficient (large) stream processing tools Web site: http://www.diku.dk/kmc 2 Regular expression Definition (Regular expression) A regular expression (RE) over alphabet (set) A is an expression of the form E; F ::= 0 j 1 j a j EjF j EF j E∗ where a 2 A. This should be read as an abstract syntax specification. Operator precedence: ∗ > juxtaposition > j. Use parentheses for associating subexpressions explicitly. A is often assumed to be finite. Kleene (1956) coined the term \regular expression". The above (though as a concrete grammar) is what he meant by it and nothing else. 3 What is (the meaning of) a regular expression? What does a regular expression denote? Regular expression as a language: A set of strings (= classical automata theory) Regular expression as a grammar or type: A set of parse trees. Regular expression as a Kleene algebra: Result of interpreting in an algebraic structure satisfying certain equational properties. Regular expression as a tool (loose notion): Domain-specific language for string processing that is embedded in or accessible from general-purpose programming language We focus on regular expressions as types, which is most relevant for extracting and transforming information from input streams. 4 Regular expression as language Definition (Language denoted by regular expression) A regular expression E denotes the language L[[E]] (set of strings) defined by L[[0]] = ; L[[EjF ]] = L[[E]] [L[[F ]] L[[1]] = fg L[[EF ]] = L[[E]] L[[F ]] S i L[[a]] = fag L[[E∗]] = i≥0(L[[E]]) where S T = fs t j s 2 S ^ t 2 T g, E 0 = fg; E i+1 = E E i . -
Formal Language (3A)
Formal Language (3A) ● Regular Language Young Won Lim 6/9/18 Copyright (c) 2018 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License". Please send corrections (or suggestions) to [email protected]. This document was produced by using LibreOffice and Octave. Young Won Lim 6/9/18 Formal Language a formal language is a set of strings of symbols together with a set of rules that are specific to it. https://en.wikipedia.org/wiki/Formal_language Young Won Lim Regular Language (3A) 3 6/9/18 Alphabet and Words The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed. The strings formed from this alphabet are called words the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas. https://en.wikipedia.org/wiki/Formal_language Young Won Lim Regular Language (3A) 4 6/9/18 Formal Language A formal language (formation rule) is often defined by means of a formal grammar such as a regular grammar or context-free grammar, https://en.wikipedia.org/wiki/Formal_language Young Won Lim Regular Language (3A) 5 6/9/18 Formal Language and Natural Language The field of formal language theory studies primarily the purely syntactical aspects of such languages— that is, their internal structural patterns. -
Regular Languageyou Can Support Wikipedia by Making a Tax-Deductible Donation
Regular languageYou can support Wikipedia by making a tax-deductible donation. From Wikipedia, the free encyclopedia "Rational language" redirects here. For the market logic concept, see Market logic. In theoretical computer science, a regular language is a formal language (i.e., a possibly infinite set of finite sequences of symbols from a finite alphabet) that satisfies the following equivalent properties: it can be accepted by a deterministic finite state machine it can be accepted by a nondeterministic finite state machine it can be accepted by an alternating finite automaton it can be described by a regular expression. Note that the "regular expression" features provided with many programming languages are augmented with features that make them capable of recognizing languages which are not regular. it can be generated by a regular grammar it can be generated by a prefix grammar it can be accepted by a read-only Turing machine it can be defined in monadic second-order logic it is recognized by some finitely generated monoid Contents 1 Regular languages over an alphabet 2 Complexity results 3 Closure properties 4 Deciding whether a language is regular 5 Finite languages 6 See also 7 References 8 External links Regular languages over an alphabet The collection of regular languages over an alphabet Σ is defined recursively as follows: the empty language Ø is a regular language. the empty string language { ε } is a regular language. For each a Σ, the singleton language { a } is a regular language. If A and B are regular languages, then A B (union), A • B (concatenation), and A* (Kleene star) are regular languages. -
The Complete Literature References
18 Annotated Bibliography The purpose of this annotated bibliography is to supply the reader with more material and with more detail than was possible in the preceding chapters, rather than to just list the works referenced in the text. The annotations cover a considerable number of subjects that have not been treated in the rest of the book. The printed version of this book includes only those literature references and their summaries that are actually referred to in it. The full literature list with summaries as far as available can be found on the web site of this book; it includes its own authors index and subject index. This annotated bibliography differs in several respects from the habitual literature list. • The annotated bibliography consists of five sections: – Main parsing material — papers about the main parsing techniques. – Further parsing material — papers about extensions of and refinements to the main parsing techniques, non-Chomsky systems, error recovery, etc. – Parser writing and application — both in computer science and in natural languages. – Support material — books and papers useful to the study of parsers. – Secondary Material — unannotated papers of peripheral interest (Internet version only). • The entries in each section have been grouped into more detailed categories; for example, the main section contains categories for general CF parsing, LR parsing, precedence parsing, etc. For details see the Table of Contents at the beginning of this book. Most publications in parsing can easily be assigned a single category. Some that span two categories have been placed in one, with a reference in the other. • The majority of the entries are annotated.