Bottom-Up Parsing Basics

1
Bottom-Up Parsing Basics
2
Example Rightmost Derivation
Input String aaabffc
S -gt ABc A -gt Aa a B -gt bF b F -gt f F
f
S gt ABc gt AbFc gt AbfFc gt Abffc gt
Aabffc gt aaabffc
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Example Symbol Stack
Input String aa abffc Symbol Stack A
The symbol stack summarizes the consumed
string.
S A B c A a
b F A a f F a f
Input String aaab ffc Symbol Stack Ab
Input String aaabff c Symbol Stack AbF
Input String aaabff c Symbol Stack AB
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Example Item (NFA state)
Input String aa abffc NFA State A -gt
A.a
The NFA state shows the part of a rule
reachable using the consumed string.
S A B c A a
b F A a f F a f
Input String aaab ffc NFA State B -gt
b.F
Input String aaabff c NFA State B -gt
bF.
Input String aaabff c NFA State S -gt
AB.c
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Example State transitions
Input String aaa bffc aaabffc aaabffc
S gt A . B c gt A b . F c gt A b f . F c

S A B c A a b
F A a f F a f
State Transition
B -gt b.F B -gt b. F -gt .f F F -gt .f
S -gt A.Bc B -gt .bF B -gt .b
b
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Symbol stack and State stack
Input String aaa b
f fc
Symbol Stack A b
f
State stack
S -gt .ABc A -gt .Aa A -gt .a
S -gt A . Bc A -gt A.a B -gt .bF B -gt .b
B -gt b.F B -gt b. F -gt . f F F -gt . f
F -gt f.F F -gt f.
A
b
f
reduce
shift
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Note 1 Redundancy

• The state stack can be generated from the
  sequence of symbols on the symbol stack, by
  tracing the derivation from the start symbol,
  using the productions.
• The state stack is used for efficiency.
• It avoids running the entire DFA (containing
  production fragments) to determine the next state
  each time.

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Why trace the entire symbol stack?
It is not possible to determine the current
production (state) by merely inspecting a fixed
number of stack symbols.
S -gt A B A -gt a A a B -gt a B
a
Input 1 a a a a Symbol Stack
a a a State
Input 2 a a a a Symbol Stack
a a a State
A -gt a . A A -gt .a
B -gt a . B B -gt .a
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DFA State Input strings with eqvt. history
RHS of rules sharing a prefix
Input String1 ab ffc Input String2 ab ge
The DFA state captures all possible rule
prefixes reachable from the start symbol using
the consumed input.
Symbol Stack A b
B -gt b.F B -gt b. F -gt . f F F -gt . f D -gt b.g

S -gt ABc ADe A -gt Aa a B -gt bF b D -gt
bg dB F -gt f F f
State
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Stacking states is adequate
S gt A B c gt A b c
S gt A D e gt A d B e gt A d b e
The effect of reduction by B -gt b depends on
the previous state.
S -gt A.Bc B -gt .b
B
b
S -gt AB.c
B -gt b.
b
D -gt d.B B -gt .b
S -gt A.De D -gt .dB D -gt .bg
d
D -gt dB.
B
D
S -gt AD.e
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Note 2 Redundancy

• The state stack contains enough information to
  regenerate the symbol stack. Note that all arcs
  into a DFA state carry the same symbol label.
• As a consequence, the symbol stack can be avoided
  by making the reduce-entry in the parse table
  specify the number of stack elements (length of
  RHS) to be popped and the (LHS) nonterminal to be
  pushed to make the transition.
• In practice, the (synthesized) semantic attribute
  associated with a stack symbol is allocated and
  computed on a parallel stack.

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Relation to Grammars

• The DFA naturally corresponds to a left-linear
  grammar.

S -gt A.Bc B -gt .b
B -gt b.
b
Grammar Rule P -gt Q b
Q
P

• The DFA state is obtained from the NFA states
  using
• the standard construction.