1. Department of Software & Media Technology
Chapter 3
Context Free Grammars
Comparison to RE Notation
Specification of Context Free Grammar Rules
Derivations & Language Defined by a Grammar
Examples
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2. Parse Trees & Abstract Syntax Trees
Examples
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3. Department of Software & Media Technology
Ambiguity
Ambiguous Grammars
Precedence and Associativity
Dangling Else Problem
Inessential Ambiguity
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4. Department of Software & Media Technology
Extended Notations
EBNF Notation
Syntax Diagrams
Examples
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5. Formal Properties of CFG
Grammar Rles as Equations
Chomsky Hierarchy
Limits of Syntax as Context Free Rules
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6. Department of Software & Media Technology
FA from Grammar
One state for each non-terminal
A rule of the form
Nt1 ::= terminal, generates transition from a state to final state
Nt1 ::= terminal Nt2
Generates transition from state 1 to state 2 on an arc labeled by the terminal
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7. Graphic representation of FA
digit
letter
underscore
identifier
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8. Department of Software & Media Technology
FA from RE
Each RE corresponds to a grammar
For all REs
A natural translation to FSM exists
Alternation often leads to non-deterministic machines
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9. Deterministic Finite Automata (DFA)
For all states S
For all characters C
There is at most one arc from any state S that is labeled with C
Easier to implement
No backtracking
Conventions for DFA:
Error transitions are not explicitly shown
Input symbols that result in the same transition are grouped together (this set can even be given a name)
Still not displayed: stopping conditions and actions
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Department of Software & Media Technology

10. Non-Deterministic Finite Automata (NFA)
A non-deterministic FA
Has at least one state
With two arcs to two distinct states
Labeled with the same character
Example: from start state, a digit can begin an integer literal or a real literal
Implementation requires backtracking
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11. Lookahead & Backtracking in NFA
letter
start
in_id
[other]
return id
finish
digit
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12. Department of Software & Media Technology
Implementation of FA
letter
start
in_id
[other]
return id
finish
digit
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13. Department of Software & Media Technology
From RE to DFA & RE to NFA
letter
start
in_id
[other]
return id
finish
digit
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14. Department of Software & Media Technology
NFA to DFA
There is an algorithm for converting a non-deterministic machine to a deterministic one
Result may have exponentially more states
Intuitively: need new states to express uncertainty about token: int or real
Other algorithms for minimizing number of states of FSM, for showing equivalence, etc.
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15. Department of Software & Media Technology
Example DFA
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16. Another view of the same DFA
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17. Yet another view of the same DFA
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18. State Minimization in DFA
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19. Department of Software & Media Technology
TINY DFA:
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20. Department of Software & Media Technology
Lex for Scanner
Lex Conventions for RE
Format of a Lex Input File
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Department of Software & Media Technology