Sohail Aslam Compiler Construction Notes Set:2-1
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Shift/Reduce Conflicts
Consider the ambiguous grammar
E → E + E | E × E | int
We will DFA state containg
[E → E × E•, +]
[E → E • + E, +]
Again we have a shift/reduce conflict. We need to reduce because × has precedence
over +
Reduce/Reduce Conflicts
If a DFA states contains both [X → α •, a] and [Y → β •, a], then on input “a” we don’t
know which production to reduce with. This is called a reduce-reduce conflict. Usually
due to gross ambiguity in the grammar.
LR(1) Table Size
LR(1) parsing table for even a simple language can be extremely large with thousands of
entries. It is possible to reduce the size of the table. Many states in the DFA are similar.
The core of set of LR items is the set of first components without the lookahead
terminals. For example the core of the item { [X → α•β, b], [Y → γ•δ, d] } is
{ X → α•β, Y → γ•δ }. Consider the LR(1) states
{ [X → α •, a], [Y → β •, c] }
{ [X → α •, b], [Y → β •, d] }
They have the same core and can be merged. The merged state contains
{ [X → α •, a/b], [Y → β •, c/d]}
These are called the LALR(1) states. LALR(1) stands for LookAhead LR(1). This leads
to tables that have 10 times fewer states than LR(1).
