Erik Jonsson School of Engineering
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Erik Jonsson School of Engineering and Computer Science. CS 4384 – 0 01. Automata Theory. http://www.utdallas.edu/~pervin. 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

CS 4384– 001

Automata Theory

http://www.utdallas.edu/~pervin

Tuesday: Context-Free Languages

Chapter Three – Review All

Thursday4-03-14

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A search of Albert Einstein's archived manuscripts last year turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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


Palindromes


Chomsky Normal Form


Other Simplifications

Useful variables and productions

Left-recursion


Useless Example


Left-recursion

3-04-14


Pushdown Automata

Many similar definitions


STACK


Odd Palindrome


Even Palindrome


CFG » PDA


PUMPING LEMMA

Context-Free


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.


Ambiguity

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


PARSING


CFG » PDA


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.

Transducer

Linz, P. 26 (Pushdown Transducer)


RPN


Linz, P. 32


Mealy machine (1955)


  • One’s Complement:

  • Increment:

Mealy Machine Examples


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


TWO’S COMPLEMENTS

CHAPTER_ONE


Review Problems


Done in class


  • Done in class


  • Done in class


Deterministic Pushdown Automata


Martin, P. 172 Corrected


Deterministic Context-Free Languages


Parsing

LL(k) Grammars


PRACTICE

CFG+PDA+CFL+PL


Sample Test


(Nothing “useless”)

Example 3.4.1 on P. 105ff M&S


End of Test!


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