'Linear grammar' presentation slideshows

Why do we care about regular languages?

Why do we care about regular languages?. Programs are composed of tokens: Identifier Number Keyword Special symbols Each of these can be defined by regular grammars . Problem: How do we handle multiple symbol operators (e.g., ++ in C, =+ in C, := in Pascal)? ?? -multiple final states?.

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Reverse of a Regular Language

Reverse of a Regular Language. Proof idea:. Construct NFA that accepts :. invert the transitions of the NFA that accepts. Theorem:. The reverse of a regular language is a regular language. Proof. Since is regular, there is NFA that accepts. Example:.

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Regular Languages and Grammars

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How to convert a left linear grammar to a right linear grammar

How to convert a left linear grammar to a right linear grammar. Roger L. Costello May 28, 2014. Objective. This mini-tutorial will answer these questions: What is a linear grammar? What is a left linear grammar? What is a right linear grammar?. Objective.

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Regular Grammars Generate Regular Languages

Regular Grammars Generate Regular Languages. Theorem. Regular grammars generate exactly the class of regular languages: If is a regular grammar then is a regular language. If is a regular language then there is a regular grammar with. Proof. First we prove:

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Linear Grammars

Linear Grammars. Grammars with at most one variable at the right side of a production Examples:. A Non-Linear Grammar. Grammar :. Number of in string. Another Linear Grammar. Grammar :. Right-Linear Grammars. All productions have form: Example:. or. string of

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Linear Grammars

Linear Grammars. Grammars with at most one variable at the right side of a production Examples:. A Non-Linear Grammar. Grammar :. Number of in string. Another Linear Grammar. Grammar :. Right-Linear Grammars. All productions have form: Example:. or. string of

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Chapter 4. Syntax Analysis (1)

Chapter 4. Syntax Analysis (1). Application of a production ?A? ? ??? in a derivation step ? i ? ? i+ 1. Formal grammars (1/3). Example : Let G 1 have N = { A , B , C }, T = { a , b , c } and the set of productions ? ? A CB ? BC A ? aABC bB ? bb

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Chapter 4. Syntax Analysis (1)

Chapter 4. Syntax Analysis (1). Application of a production ?A? ? ??? in a derivation step ? i ? ? i+ 1. Formal grammars (1/3). Example : Let G 1 have N = { A , B , C }, T = { a , b , c } and the set of productions ? ? A CB ? BC A ? aABC bB ? bb

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????? ????

????? ????. ????? ?? ????. ???? ??? Generalized transition graph ??? ??? ?? ??? ???? ?? ??? ??? ?? ?????? ?? <= ? ??? ?? ??? ?? . a -> a a, b -> a + b. Figure 3.8. a. c*. a + b. L(a* + a*(a + b)c*). Figure 3.9. e. d. c. qj. qi. q. b. a. ce*b. ae*d. ce*d. qj. qi. ae*b.

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Lecture#14-15

Lecture#14-15. Grammar. A grammar G = (V, T, S, P) consists of the following quadruple: a set V of variables (non-terminal symbols), including a starting symbol S ? NT a set T of terminals (same as an alphabet, ?) A start symbol S ? V a set P of production rules Example: S ? aS | A

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CSA2050 Introduction to Computational Linguistics

CSA2050 Introduction to Computational Linguistics. Parsing I. Why Is Syntax Important?. The presidential candidate who was extremely popular smiled broadly. How many presidential candidates are implied? 1 or >1?. Why Is Syntax Important?.

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Context-free Grammars

Context-free Grammars. Recursive definition Grammar Derivation. What is the syntax of the description (meta-language)? External form of the grammar How do we associate a language with such a description? Semantics or use of the grammar

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Chapter 4. Syntax Analysis (1)

Chapter 4. Syntax Analysis (1). Application of a production ?A? ? ??? in a derivation step ? i ? ? i+ 1. Formal grammars (1/3). Example : Let G 1 have N = { A , B , C }, T = { a , b , c } and the set of productions ? ? A CB ? BC A ? aABC bB ? bb

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Lecture 11 Context-Free Grammar

Lecture 11 Context-Free Grammar. Definition. A context-free grammar (CFG) G is a quadruple (V, ? , R, S) where V : a set of non-terminal symbols ? : a set of terminals ( V ? ? = ? ) R : a set of rules ( R: V ? (V U ? )* ) S : a start symbol. Example. V = {q, f,} ? = {0, 1}

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Regular Grammars

Regular Grammars. Lecture 11 Naveen Z Quazilbash. Overview. Examples Definition Language defined by the grammar Linearity of grammar Equivalence with NFAs. Examples. Example 1: S ? aAb A?cA A? ? The corresponding language is ac*b Example 2: S ? aA A? bB B?aA B ? ?

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Linear Grammars

Linear Grammars. Grammars with at most one variable at the right side of a production Examples:. A Non-Linear Grammar. Grammar :. Number of in string. Another Linear Grammar. Grammar :. Right-Linear Grammars. All productions have form: Example:. or. string of

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Regular Grammars

Regular Grammars. Right-linear Grammar. A grammar G=(V,T,S,P) is right-linear if all productions are of the form A -> xB, or A -> x where A,B ? V, and x ? T*. Language of RL Grammar. Claim: For all right-linear grammars G, L(G) is regular Proof by construction. A RL Grammar for a RL.

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