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Erik Jonsson School of Engineering and Computer Science. CS 4384 – 0 01. Automata Theory. Tuesday: Context-Free Languages Chapter Three – Review All. Thursday 4-03-14. FEARLESS Engineering.

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Erik Jonsson School of Engineering and Computer Science

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Erik Jonsson School of Engineering

and Computer Science

CS 4384– 001

Automata Theory

Tuesday: Context-Free Languages

Chapter Three – Review All


FEARLESS Engineering

A search of Albert Einstein's archived manuscripts last year turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe. Einstein was attempting to make sense of Edwin Hubble's observation that the universe was expanding, but he made a mathematical error. When he discovered his mistake, he set aside the paper, which is now in a digital archive of his papers at the Hebrew University in Jerusalem. Waterford Institute of Technology physicist Cormac O'Raifeartaigh and colleagues found the paper while scouring the archive.

Context-free Languages

Chapter Three


Chomsky Normal Form

Other Simplifications

Useful variables and productions


Useless Example



Pushdown Automata

Many similar definitions


Odd Palindrome

Even Palindrome




NOTE: CFLs are not closed under intersection (or complement)!

Martin, P. 218; H&U, P. 115

CS 341 – UT-Austin

CS 341 – UT-Austin

Informal Verbal PDAs

Read and push a’s onto the stack; read b’s and match them against the stack until empty; read any additional b’s and push them onto the stack; read and match c’s with stack exactly.

For each a read, non-deterministically push ONE or TWO a’s on the stack; then match b’s read exactly with stack.


Dangling ELSE Problem

“An ELSE belongs to the last preceding IF for which there is no ELSE already”

Deterministic Pushdown Automata

Martin, P. 172 Corrected

End of File (EOF):

UNIX Control-D (ASCII 04)

Windows Control-Z (ASCII 26)

Java’s Buffered Reader Null (ASCII 0)

Empty Stack ($), (Zo)

End of File; Empty Stack



S -> aSb | ab => S -> X_aY | X_aX_b ; Y -> SX_b;

X_a -> a ; X_b -> b

What if more than four characters needed?

  • An automaton whose output response is limited to a simple “yes” or “no” is called an accepter. Presented with an input string, an accepter either accepts (recognizes) the string or rejects it.

  • A more general automaton, capable of producing strings of symbols as output, is called a transducer.


Linz, P. 26 (Pushdown Transducer)


Linz, P. 32

Mealy machine (1955)

  • One’s Complement:

  • Increment:

Mealy Machine Examples

Note: You can combine the START and C states and get:



Review Problems

Done in class

  • Done in class

  • Done in class

Deterministic Pushdown Automata

Martin, P. 172 Corrected

Deterministic Context-Free Languages


LL(k) Grammars



Sample Test

(Nothing “useless”)

Example 3.4.1 on P. 105ff M&S

End of Test!

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