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Table of contents
Augmented Grammar
Steps for Constructing the LR Parsing Table
Fill the Table: For each state
Construct an LR Parsing Table for the Given Context-Free Grammar
Initial State (I0)
Creating New States
Completing the Table
Finalizing Actions
Frequently Asked Questions
What does the dot mean in LR parsing tables?
Why do we need augmented grammar in LR parsing?
How can errors in input affect LR parsing?
Last Updated: May 27, 2024

LR (0) Parser

Author Sinki Kumari
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LR(0) parsers are foundational tools in the field of compiler design, serving a critical role in syntax analysis. This type of parser uses a specific set of rules & procedures to analyze the grammatical structure of programming languages. Essentially, it helps in determining whether a string of symbols can be generated by a grammar. 

LR (0) Parser

This article will talk about the main concepts of LR(0) parsing, its operation, & how it applies to compiler construction. 

Augmented Grammar

Augmented grammar is a technique used in compiler construction to enhance the original grammar of a programming language for easier parsing. It involves adding a new production rule that does not interfere with the existing grammar rules but helps the parser recognize when the input has been completely parsed. For LR(0) parsers, this addition simplifies the construction of parsing tables & aids in the handling of ambiguous or incomplete parsing scenarios.

To illustrate, consider a simple grammar:

S -> AA
A -> aA | b

For augmented grammar, we add a new start symbol (let's say S') & a production:

S' -> S

This change means that our parser now starts with S' & successfully ends when it derives S, marking the end of parsing. This small addition helps manage the parsing process more smoothly & reduces errors during syntax analysis.

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Steps for Constructing the LR Parsing Table

Creating an LR(0) parsing table is a systematic process that involves several clear steps. This table is crucial because it guides the parser on what action to take (shift, reduce, or accept) based on the current state & the next input symbol. Here’s how to construct one:

  • Identify the States: Each state in the LR parsing table represents a possible situation in the parsing process. You start with the initial state that includes the augmented grammar starting with the dot at the beginning.
  • Closure Operation: For each state, apply the closure operation. If there is a production like A -> .Bα in a state & a grammar rule B -> γ, then add B -> .γ to the same state. This step extends the state with new items that could be derived from the current symbol next to the dot.
  • Goto Operation: This involves moving the dot past a symbol. For example, if you have A -> .Bα in a state, the Goto operation would create or shift to a new state with A -> B.α. Each of these movements corresponds to a transition in the parsing table under the column for the symbol just passed.

Fill the Table: For each state

  • If the dot is at the end of a production, mark it as a reduction by that production.
  • If the dot is before a symbol, enter a shift instruction in the table under the column for that symbol.
  • If the dot can immediately precede the end of the input in any configuration, mark this as an accept.

Construct an LR Parsing Table for the Given Context-Free Grammar

To construct an LR parsing table for the given grammar rules:

S -> AA
A -> aA | b

we follow a structured method to visualize how the parser reacts to various inputs based on the grammar. Let’s see how the construction process works:

Initial State (I0)

  • Start with the augmented grammar: S' -> .S
  • Apply closure to include all possible beginnings of S: S -> .AA
  • Include productions from A because AA starts with A: A -> .aA and A -> .b

This state suggests that if an 'a' or 'b' is seen, moves should be made to handle these possibilities.

Creating New States

  • From I0, on seeing 'a', shift to a new state (I1) with A -> a.A
  • Apply closure on I1 to include the continuations of A -> a.A: A -> .aA, A -> .b
  • From I0, on seeing 'b', shift to a new state (I2) with A -> b.

Completing the Table

  • For reductions, in I2, since we see A -> b., reduce by the rule A -> b.
  • For shifts, from I1 on seeing 'a' again, move to a new state or back to an existing state that represents A -> a.A
  • Continue this process for each symbol in the grammar, transitioning between states based on the input and marking reductions where the production rules are completed.

Finalizing Actions

  • Each entry in the table corresponds to either a shift (moving to another state), a reduction (applying a grammar rule), or an accept (successfully recognizing the input).
  • The parser uses this table to decide what action to take as it reads through the input string.

Here is a simplified representation of some parts of the LR table:

I2  R2  
I3    R1
I4    Acc

This table is crucial for the parser to determine the correct sequences of actions to process the input according to the defined grammar, ensuring that the syntax of the language is adhered to.

Frequently Asked Questions

What does the dot mean in LR parsing tables?

The dot in an LR parsing table represents the current position of the parser in a production rule. It indicates which symbols have been successfully parsed and which are yet to be processed.

Why do we need augmented grammar in LR parsing?

Augmented grammar adds a new production rule at the beginning of the original grammar. This helps the parser recognize when it has successfully parsed the entire input, marking the specific completion point.

How can errors in input affect LR parsing?

Errors in the input can lead to situations where the parsing table specifies no valid actions (shift, reduce, or accept). This typically triggers error handling routines in the parser to either recover from the error or report it.


In this article, we have learned the basics of LR(0) parsers, the role of augmented grammar, and the systematic approach to constructing an LR parsing table. We discussed how these components work together to facilitate the syntax analysis phase in compiler design, ensuring that programming languages are parsed accurately and efficiently. These concepts helps developers to understand how compilers translate code into machine-readable formats, which is very essential for software development and programming language design.

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