Bottom Up Parsing
With Examples

BOTTOM UP PARSING
• A bottom-up parsing constructs the parse tree for an input string beginning from the bottom
(the leaves) and moves to work towards the top (the root).
• Bottom-up parsing is a parser that reduces the string to the start symbol of the grammar.
 TYPE OF BOTTOM UP PARSER:

DIFFERENCE BETWEEN LR(0) AND LR(1)
CANONICAL ITEM SET:
 Unlike LR(0) canonical item set, in LR(1) canonical item set
each time the look-ahead has to be maintained even in the
produced productions.
 The look-ahead of the produced productions depends on
the First (leftover of the production producing it).

GRAMMAR 1 (LR(0))
1. S  AA
A  aA / b
Checking this grammar for
LR(0)
Augmented grammar –
S’ -> . S
S -> . AA ---(1)
A -> . aA ---(2)
A -> . b ---(3)
Steps for constructing the LR parsing
table :
• Writing augmented grammar &
check ambiguity
• LR(0) collection of items to be
found
• Defining 2 functions: goto(list of
terminals) and action(list of non-
terminals) in the parsing table.
 The terminals of this grammar are {a, b}
 The non-terminals of this grammar are {S, A}

COLLECTION OF CANONICAL ITEMS
GRAMMAR 1

STATE ACTION GOTO
a b $ A S
I0 S3 S4 2 1
I1 Accept
I2 S3 S4 5
I3 S3 S4 6
I4 r3 r3 r3
I5 r1 r1 r1
I6 r2 r2 r2
PARSING TABLE
Since there is no conflict like S-R or S-S,
we can say this is a LR(0) grammar.
GRAMMAR 1
COLLECTION OF ITEMS

Now we will parse an input string & create parse tree:
GRAMMAR 1
PARSING STACK INPUT ACTION
1 $0 aabb$ Shift a3
2 $0a3 abb$ Shift a3
3 $0a3a3 bb$ Shift b4
4 $0a3a3b4 b$ reduce r3 (A -> b)
5 $0a3a3A6 b$ reduce r2 (A -> aA)
6 $0a3A6 b$ reduce r2 (A -> aA)
7 $0A2 b$ Shift b4
8 $0A2b4 $ reduce r3 (A -> b)
9 $0A2A5 $ reduce r1 (S -> AA)
10 $0S1 $ Accept

GRAMMAR 1
PARSE TREE

GRAMMAR 2 (CLR(1))
2. E  BB
B  cB / d
Checking this grammar for LR(1):
The step involves in CLR(1) parsing is given below:
•Write a CFG for the given input string
•Check if the grammar is ambiguous or not.
•Add an augmented grammar.
•Create a canonical LR(1) item.
•Draw DFA
•Construct an CLR(1) parsing table.
Augmented grammar –
E’ -> . E, $
E -> . BB, $
B -> . cB / .d, c/d

GRAMMAR 2
CLR(1) DIAGRAM

GRAMMAR 2
STATE ACTION GOTO
c d $ E B
I0 S3 S4 1 2
I1 Accept
I2 S6 S7 5
I3 S3 S4 8
I4 r3 r3
I5 r1
I6 S6 S7 9
I7 r3
I8 r2 r2
I9 r2
PARSING TABLE
This is a LR(1) grammar.
COLLECTION OF ITEMS

GATE QUESTIONS
 Which of the following statements about parser is/are CORRECT?
I. Canonical LR is more powerful than SLR.
II. SLR is more powerful than LALR.
III. SLR is more powerful than Canonical LR.?
(A) I only
(B) II only
(C) III only
(D) II & III both
• Answer: (A)
• Explanation: LR parsers in terms of their power:
CLR > LALR > SLR > LR (0)

GATE QUESTIONS
A bottom-up parser generates :
(A) Left-most derivation in reverse
(B) Right-most derivation in reverse
(C) Correct Answer
(D) Left-most derivation
• Answer: (B)

 What is the maximum number of reduce moves that can be taken by a bottom-up
parser for a grammar with no epsilon- and unit-production (i.e., of type A -> є and
A -> a) to parse a string with n tokens?
(A) n/2 (B) n-1 (C) 2n-1 (D) 2n
• Answer: (B)
• Explanation: Maximum number of reduce moves : Only one terminal is
reduced and last 2 tokens will take only 1 move. Input string of n tokens: n-
2+1 = n-1 reduce moves.
GATE QUESTIONS

 Consider the following Syntax Directed Translation Scheme (SDTS), with non-terminals {S, A}
and terminals {a, b}.
S → aA {print 1}
S → a {print 2}
A → Sb {print 3}
Using the above SDTS, the output printed by a bottom-up parser, for the input aab is:
(A) 1 3 2 (B) 2 2 3 (C) 2 3 1 (D) Syntax error
GATE QUESTIONS
Answer: (C)
Explanation: In parse tree, we stopped at
‘aab’ because it matches with the required
string. It prints the output string from
bottom to top i.e. 2 3 1

GATE QUESTIONS
 Which of the following statements is false?
A) An unambiguous grammar has same leftmost and rightmost derivation
B) An LL(1) parser is a top-down parser
C) LALR is more powerful than SLR
D) An ambiguous grammar can never be LR(k) for any k
Answer: (A)