Earley parser

The algorithm is hard to see from the abstract description above. It becomes much clearer how it operates once you see it in action. The output is a little verbose, but you should be able to follow it. Let's say you have the following simple arithmetic grammar: P → S # the start rule S → S + M | M M → M * T | T T → number And you have the input: 2 + 3 * 4 ...

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Earley parser, Earley parser - Performing the Algorithm, Earley parser - Example

Read more here: » Earley parser: Encyclopedia II - Earley parser - Example

In linguistics and computer science, a context-free grammar (CFG) is a formal grammar in which every production rule is of the form V → w where V is a non-terminal symbol and w is a string consisting of terminals and/or non-terminals. The term "context-free" comes from the fact that the non-terminal V can always be replaced by w, regardless of the context in which it occurs. A formal language is context ...

Including:

• Context-free grammar - Formal definition
• Context-free grammar - Examples
• Context-free grammar - Example 1
• Context-free grammar - Example 2
• Context-free grammar - Example 3
• Context-free grammar - Example 4
• Context-free grammar - Other examples
• Context-free grammar - Derivations and syntax trees
• Context-free grammar - Normal forms
• Context-free grammar - Undecidable problems
• Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia - Context-free grammar

The example below demonstrates the common case of parsing a language with two levels of grammar: lexical and syntactic. The first stage is the token generation, or lexical parse phase. For example, a calculator program would look at an input such as "12*(3+4)^2" and split it into the tokens 12, *, (, 3, +, 4, ), ^ and 2, each of which is a meaningful symbol in the context of an arithmetic expression. The parser would contain rules to tell it that the characters *, +, ^, ( and ) mark the start of a new token, so meaningless t ...

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Parsing, Parsing - Human languages, Parsing - Programming languages, Parsing - Overview of process, Parsing - Types of parsers, Parsing - Examples of parsers, Parsing - Top-down parsers, Parsing - Bottom-up parsers

Read more here: » Parsing: Encyclopedia II - Parsing - Overview of process

There are basically two ways to describe how in a certain grammar a string can be derived from the start symbol. The simplest way is to list the consecutive strings of symbols, beginning with the start symbol and ending with the string, and the rules that have been applied. If we introduce a strategy such as "always replace the left-most nonterminal first" then for context-free grammars the list of applied grammar rules is by itself sufficient. This is called the leftmost derivation of a string. For example, if we take the follow ...

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Context-free grammar, Context-free grammar - Formal definition, Context-free grammar - Examples, Context-free grammar - Example 1, Context-free grammar - Example 2, Context-free grammar - Example 3, Context-free grammar - Example 4, Context-free grammar - Other examples, Context-free grammar - Derivations and syntax trees, Context-free grammar - Normal forms, Context-free grammar - Undecidable problems, Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia II - Context-free grammar - Derivations and syntax trees

The example below demonstrates the common case of parsing a language with two levels of grammar: lexical and syntactic. The first stage is the token generation, or lexical parse phase. For example, a calculator program would look at an input such as "12*(3+4)^2" and split it into the tokens 12, *, (, 3, +, 4, ), ^ and 2, each of which is a meaningful symbol in the context of an arithmetic expression. The parser would contain rules to tell it that the characters *, +, ^, ( and ) mark the start of a new token, so meaningless ...

See also:

Parsing, Parsing - Human languages, Parsing - Programming languages, Parsing - Overview of process, Parsing - Types of parsers, Parsing - Examples of parsers, Parsing - Top-down parsers, Parsing - Bottom-up parsers

Read more here: » Parsing: Encyclopedia II - Parsing - Overview of process

Parsing - Top-down parsers. Some of the parsers that use top-down parsing include: Recursive descent parser LL parser Packrat parser Unger parser Parsing - Bottom-up parsers. Some of the parsers that use bottom-up parsing include: LR parser SLR parser LALR parser Canonical LR parser GLR parser See also:

Parsing, Parsing - Human languages, Parsing - Programming languages, Parsing - Overview of process, Parsing - Types of parsers, Parsing - Examples of parsers, Parsing - Top-down parsers, Parsing - Bottom-up parsers

Read more here: » Parsing: Encyclopedia II - Parsing - Examples of parsers

The task of the parser is essentially to determine if and how the input can be derived from the start symbol within the rules of the formal grammar. This can be done in essentially two ways: Top-down parsing - A parser can start with the start symbol and try to transform it to the input. Intuitively, the parser starts from the largest elements and breaks them down into incrementally smaller parts. LL parsers are examples of top-down parsers. Bottom-up parsing - A parser can start with the input and attempt to rewrite it ...

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Parsing, Parsing - Human languages, Parsing - Programming languages, Parsing - Overview of process, Parsing - Types of parsers, Parsing - Examples of parsers, Parsing - Top-down parsers, Parsing - Bottom-up parsers

Read more here: » Parsing: Encyclopedia II - Parsing - Types of parsers

Some of the parsers that use top-down parsing include: Recursive descent parser LL parser Packrat parser Unger parser Parsing - Bottom-up parsers . Some of the parsers that use bottom-up parsing include: LR parser SLR parser LALR parser Canonical LR parser GLR parser Earley parser CYK parser ...

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Parsing, Parsing - Human languages, Parsing - Programming languages, Parsing - Overview of process, Parsing - Types of parsers, Parsing - Examples of parsers, Parsing - Top-down parsers, Parsing - Bottom-up parsers

Read more here: » Parsing: Encyclopedia II - Parsing - Examples of parsers

Context-free grammar - Example 1. A simple context-free grammar is S → aSb | ε where | is a logical OR, and is used to separate multiple options for the same non-terminal—ε stands for an empty string. This grammar generates the language which is not regular. Context-free grammar - Example 2. Here is a context-free grammar for syntactically correct infix algebraic expressions in the variables x, y and z: S → x | y | z | S + S | S - S | S * S | S/S | (S) This grammar can, for example, generat ...

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Context-free grammar, Context-free grammar - Formal definition, Context-free grammar - Examples, Context-free grammar - Example 1, Context-free grammar - Example 2, Context-free grammar - Example 3, Context-free grammar - Example 4, Context-free grammar - Other examples, Context-free grammar - Derivations and syntax trees, Context-free grammar - Normal forms, Context-free grammar - Undecidable problems, Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia II - Context-free grammar - Examples

Just as any formal grammar, a context-free grammar G can be defined as a 4-tuple: G = (Vt,Vn,P,S) where Vt is a finite set of terminals Vn is a finite set of non-terminals P is a finite set of productions rules S is an e ...

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Context-free grammar, Context-free grammar - Formal definition, Context-free grammar - Examples, Context-free grammar - Example 1, Context-free grammar - Example 2, Context-free grammar - Example 3, Context-free grammar - Example 4, Context-free grammar - Other examples, Context-free grammar - Derivations and syntax trees, Context-free grammar - Normal forms, Context-free grammar - Undecidable problems, Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia II - Context-free grammar - Formal definition

Every context-free grammar which does not generate the empty string can be transformed into an equivalent one in Chomsky normal form or Greibach normal form. "Equivalent" here means that the two grammars generate the same language. Because of the especially simple form of production rules in Chomsky Normal Form grammars, this normal form has both theoretical and practical implications. For instance, given a context-free grammar, one can use the Chomsky Normal Form to construct a polynomial-time algorithm which decides whether a given string is in the language re ...

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Context-free grammar, Context-free grammar - Formal definition, Context-free grammar - Examples, Context-free grammar - Example 1, Context-free grammar - Example 2, Context-free grammar - Example 3, Context-free grammar - Example 4, Context-free grammar - Other examples, Context-free grammar - Derivations and syntax trees, Context-free grammar - Normal forms, Context-free grammar - Undecidable problems, Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia II - Context-free grammar - Normal forms

Although some operations on context-free grammars are decidable due to their limited power, unlike finite automata CFGs do have interesting undecidable problems. One of the simplest and most cited is the problem of deciding whether a CFG accepts the language of all strings. A reduction can be demonstrated to this problem from the well-known undecidable problem of determining whether a Turing machine accepts a particular input. The reduction uses the concept of a computation history, a string describing an entire computation of a Turin ...

See also:

Context-free grammar, Context-free grammar - Formal definition, Context-free grammar - Examples, Context-free grammar - Example 1, Context-free grammar - Example 2, Context-free grammar - Example 3, Context-free grammar - Example 4, Context-free grammar - Other examples, Context-free grammar - Derivations and syntax trees, Context-free grammar - Normal forms, Context-free grammar - Undecidable problems, Context-free grammar - Properties of context-free languages

Read more here: » Context-free grammar: Encyclopedia II - Context-free grammar - Undecidable problems

To understand how Earley's algorithm executes, you have to understand dot notation. Given a production A → BCD (where B, C, and D are symbols in the grammar, terminals or nonterminals), the notation A → B • C D represents a condition in which B has already been parsed and the sequence C D is expected. For every input position (which represents a position between tokens), the parser generates a state set. Each state is the cartesian product (that is, just the combination) of: A dot condition for a particular production. The position at which the matching ...

See also:

Earley parser, Earley parser - Performing the Algorithm, Earley parser - Example

Read more here: » Earley parser: Encyclopedia II - Earley parser - Performing the Algorithm