© Oscar Nierstrasz Compiler Construction

Context-free grammars

1. <goal> := <expr>2. <expr> := <expr> <op> <term>3. | <term>4. <term> := number5. | id6. <op> := +7. | -

Context-free syntax is specified with a grammar, usually in Backus-Naur form (BNF)

A grammar G = (S,N,T,P)• S is the start-symbol• N is a set of non-terminal symbols• T is a set of terminal symbols• P is a set of productions — P: N (N T)*

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2

Deterministic Finite Automata - Definition

• A Deterministic Finite Automaton (DFA) consists of:– Q ==> a finite set of states– ∑ ==> a finite set of input symbols (alphabet)– q0 ==> a start state– F ==> set of final states– δ ==> a transition function, which is a mapping between Q

x ∑ ==> Q• A DFA is defined by the 5-tuple:

– {Q, ∑ , q0,F, δ }

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Regular Languages

• Let L(A) be a language recognized by a DFA A. – Then L(A) is called a “Regular Language”.

• Locate regular languages in the Chomsky Hierarchy

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Non-deterministic Finite Automata (NFA)

• A Non-deterministic Finite Automaton (NFA) – is of course “non-deterministic”

• Implying that the machine can exist in more than one state at the same time

• Transitions could be non-deterministic

qi

1

1

qj

qk

… • Each transition function therefore maps to a set of states

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Non-deterministic Finite Automata (NFA)

• A Non-deterministic Finite Automaton (NFA) consists of:– Q ==> a finite set of states– ∑ ==> a finite set of input symbols (alphabet)– q0 ==> a start state– F ==> set of final states – δ ==> a transition function, which is a mapping between Q

x ∑ ==> subset of Q• An NFA is also defined by the 5-tuple:

– {Q, ∑ , q0,F, δ }

22.04.2023 Dr. S. Nadeem Ahsan, IQRA-University 6

NFA Construction

• Automatic construction example

• a(b*c)

• a(b|c+)?Build a Disjunction

Conversion Example – continued (4)

StateInput Symbol

a b

A B C B B D C B C

E B C D B E

A

C

B D Estart bb

b

b

b

aa

a

a

This gives the transition table for the DFA of: