The document discusses ambiguous grammars in computer science, defining a context-free grammar as ambiguous if a string can be derived in multiple ways, which poses challenges for compilers requiring semantic context to resolve ambiguities. It also explains deterministic finite automata (DFA) and Simple LR (SLR) parsing, highlighting the differences and processes involved in parsing, including the construction of parsing tables and use of canonical collections of LR(0) items. The document concludes with the construction techniques and characteristics of SLR parsing, emphasizing its role as a superset of all LR(0) grammars.

1. Topics: Ambiguous Grammar, DFA and SLR grammar.
Ismail Mohamed mohamud (maahir)
Abdiwahid farah isse
Abdifitah Awil Ahmed
Abdinor mohaedAhmed
Abdinasir nor kadie
Group five

2. Ambiguous Grammar
In computer science, a context-free grammar is said to be an ambiguous grammar if
there exists a string which can be generated by the grammar in more than one way (i.e.,
the string admits more than one parse tree or, equivalently, more than one leftmost
derivation). A context-free language is inherently ambiguous if all context- free
grammars generating that language are ambiguous.

3. Ambiguous Grammar
Some programming languages have ambiguous grammars; in this case, semantic
information is needed to select the intended parse tree of an ambiguous construct.
can be interpreted as either.
the declaration of an identifier named y of type pointer-to-x, or
an expression in which x is multiplied by y and then the result is discarded.
To correctly choose between the two possible interpretations, a compiler must
consult its symbol table to find out whether x has been declared as a type def
name that is visible at this point.

4. Ambiguous Grammar
A CFG is said to be ambiguous if and only if it contains more than one derivation
trees for same string.
Definition of Ambiguous Grammar: Let G = (N,T, P, S ) be a CFG. A string w
∈ L(G) is said to be “ambiguously derivable “if there are two or more different
derivation trees for that string in G.
Definition of Ambiguous Grammar: A CFG given by G = (N, T, P, S) is said to
be “ambiguous” if there exists at least one string in L(G) which is ambiguously
derivable. Otherwise it is unambiguous.

5. Ambiguous Grammar
Ambiguity is a property of a grammar, and it is usually, but not always possible to find
an equivalent unambiguous grammar.
An “ inherantly ambiguous language” is a language for which no unambiguous
grammar exists.
Solved Example:
Show that the grammar G with production
S → a | aAb | abSb
A → aAAb | bS
is ambiguous.

6. Ambiguous Grammar
Solution:
S ⟹ abSb ( ∵ S → abSb)
⟹ abab (∵ S → a)
Similarly,
S ⟹ aAb ( ∵ S → aAb)
⟹ abSb (∵ A → bS)
⟹ abab (∵ S → a)
Since ‘abab’ has two different derivations, the grammar G is ambiguous.
Proof of CFG is ambiguous or not by using parse tree solved example:
Consider the grammar G with production:
S → aSS
S → b

7. Ambiguous Grammar
• The parse trees are as follows.
• Top down Parsing: Sequence of rules are applied in a leftmost derivation in Top
down parsing.
•
Bottom-up Parsing: Sequence of rules are applied in a rightmost derivation in
Bottom-up parsing.

8. Deterministic finite Automata
DFArefers to deterministic finite automata. Deterministicrefers to theuniquenessof the
computation.Thefinite automata are called deterministic finite automata if themachineis read an
input string onesymbolat a time.
InDFA,there isonly onepath for specific input from thecurrentstate to thenext state.
DFAdoesnotaccept thenullmove,i.e., theDFAcannotchangestate without any input character
DFAcancontain multiple final states.It isusedinLexicalAnalysisinCompiler.

9. Deterministic finite Automata
A DFAcanberepresentedby digraphs calledstatediagram.In which:
Thestate isrepresented byvertices.
Thearc labeled with aninput character showthe transitions.
Theinitial state ismarked with anarrow.
Thefinal state isdenoted by a doublecircle.

10. SIMPLE LR PARSING SLR
SLR refers to simpleLRParsing.It issameasLR(0)parsing. Theonly difference isintheparsing
table. T
oconstructSLR(1) parsing table, weusecanonical collection of LR(0) item.
IntheSLR(1) parsing, weplace thereducemoveonly inthefollow of left hand side.
Various stepsinvolved in theSLR(1) Parsing:
Forthegiven input string write a context free grammar
Checktheambiguity of the grammar
AddAugmentproductioninthegiven grammar
Create Canonicalcollection of LR(0) items
Draw a data flow diagram (DFA)
Constructa SLR(1) parsing table

11. Constructing SLR Parsing Tables – LR(0) Item
An LR(0) item of a grammar G is a production of G a dot at the
some position of the right side.
Ex:
A → aBb
Possible LR(0) Items:
A → ∙ aBb
(four different possibility)
A → a ∙ Bb
A → aB ∙ b
A → aBb

12. Constructing SLR Parsing Tables – LR(0) Item
Sets of LR(0) items will be the states of action and goto table of
the SLR parser.
States represent sets of “items”
LR parser makes shift-reduce decision by maintaining states to
keep track of where we are in a parsing process
SLR grammars are a superset of all LR(0) grammars
In the LR parsing,
"L" stands for left-to-right scanning of the input.
"R" stands for constructing a right most derivation in reverse.

13. Constructing SLR Parsing Tables
A collection of sets of LR(0) items (the canonical LR(0)
collection) is the basis for constructing SLR parsers.
Canonical LR(0) collection provides the basis of constructing a
DFA called LR(0) automaton
This DFA is used to make parsing decisions
Each state of LR(0) automaton represents a set of items in the
canonical LR(0) collection