An efficient bottom-up syntax analysis technique that can be used CFG is called LR(k) parsing. The ‘L’ is for left-to-right scanning of the input, the ‘R’ for constructing a rightmost derivation in reverse, and the ‘k’ for the number of input symbols. When ‘k’ is omitted, it is

assumed to be 1.

Advantages of LR parsing:

1. It recognizes virtually all programming language constructs for which CFG can be written.

2.     It is an efficient non-backtracking shift-reduce parsing method.

3.     A grammar that can be parsed using LR method is a proper superset of a grammar that can be parsed with predictive parser

4.     4. It detects a syntactic error as soon as possible.

Drawbacks of LR method:

 It is too much of work to construct a LR parser by hand for a programming language grammar. A specialized tool, called a LR parser generator, is needed. Example: YACC.

Types of LR parsing method:

1. SLR- Simple LR

Easiest to implement, least powerful.

2. CLR- Canonical LR

Most powerful, most expensive.

3. LALR- Look-Ahead LR

Intermediate in size and cost between the other two methods.

The LR parsing algorithm:

The schematic form of an LR parser is as follows:

Fig. 2.5 Model of an LR parser

It consists of an input, an output, a stack, a driver program, and a pa parts (action and goto).

Ø     The driver program is the same for all LR parser.

Ø     The parsing program reads characters from an input buffer one at a time.

Ø     The program uses a stack to store a string of the form s0X1s1X2s2…Xmsm, where sm is on top. Each Xi is a grammar symbol and each si is a state.

Ø     The parsing table consists of two parts : action and goto functions.

Action : The parsing program determines sm, the state currently on top of stack, and ai, the current input symbol. It then consults action[sm,ai] in the action table which can have one of four values:

1. shift s, where s is a state,

2. reduce by a grammar production A → β, 

3. accept, 

4. 4. error.

Goto : The function goto takes a state and grammar symbol as arguments and produces a state.

LR Parsing algorithm:

 Input: An input string w and an LR parsing table with functions action and goto for grammar G. Output: If w is in L(G), a bottom-up-parse for w; otherwise, an error indication.

 Method: Initially, the parser has s0 on its stack, where s0 is the initial state, and w$ in the input buffer. The parser then executes the following program:

 set ip to point to the first input symbol of w$; repeat forever begin

let s be the state on top of the stack and

a the symbol pointed to by ip;

 if action[s, a] = shift s’ then begin

 push a then s’ on top of the stack; advance ip to the next input symbol end

else if action[s, a] = reduce A→β then begin pop 2* | β | symbols off the stack;

let s’ be the state now on top of the stack; push A then goto[s’, A] on top of the stack; output the production A→ β


else if action[s, a] = accept then


else error( )


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