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A search of Albert Einstein's archived manuscripts last year turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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

Context-free Languages turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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.

Chapter Three


Palindromes turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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.


Chomsky normal form
Chomsky Normal Form 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.


O ther simplifications

O 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.ther Simplifications

Useful variables and productions

Left-recursion


Useless example
Useless Example 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.


Left recursion
Left-recursion 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.

3-04-14


Pushdown automata

Pushdown Automata 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.

Many similar definitions


Stack
STACK 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.


Odd Palindrome 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.


Even Palindrome 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.


Cfg pda
CFG » PDA 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.


Pumping lemma

PUMPING LEMMA 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




CS 341 – UT-Austin complement)!


CS 341 – UT-Austin complement)!


Informal verbal pdas
Informal Verbal PDAs complement)!


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

Ambiguity on the stack; then match b’s read exactly with stack.

Dangling ELSE Problem


on the stack; then match b’s read exactly with stack.An ELSE belongs to the last preceding IF for which there is no ELSE already”


Deterministic pushdown automata

Deterministic Pushdown Automata on the stack; then match b’s read exactly with stack.


Martin, P. 172 Corrected on the stack; then match b’s read exactly with stack.


End of file empty stack

End of File (EOF): on the stack; then match b’s read exactly with stack.

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
PARSING on the stack; then match b’s read exactly with stack.


Cfg pda1
CFG » PDA on the stack; then match b’s read exactly with stack.


S -> on the stack; then match b’s read exactly with stack.aSb | ab => S -> X_aY | X_aX_b ; Y -> SX_b;

X_a -> a ; X_b -> b


What if more than four characters needed? on the stack; then match b’s read exactly with stack.


Transducer

  • 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 “yes” or “no” is called an


Linz, P. 32 “yes” or “no” is called an


Mealy machine (1955) “yes” or “no” is called an


Mealy machine examples

Mealy Machine Examples


Note: You can combine the START and C states and get: “yes” or “no” is called an


Two s complements

TWO’S COMPLEMENTS “yes” or “no” is called an

CHAPTER_ONE


Review problems
Review Problems “yes” or “no” is called an


Done in class “yes” or “no” is called an


  • Done in “yes” or “no” is called an class


  • Done in “yes” or “no” is called an class


Deterministic pushdown automata1

Deterministic Pushdown Automata “yes” or “no” is called an


Martin, P. 172 Corrected “yes” or “no” is called an


Deterministic context free languages
Deterministic Context-Free Languages “yes” or “no” is called an


Parsing1
Parsing “yes” or “no” is called an

LL(k) Grammars


Practice

PRACTICE “yes” or “no” is called an

CFG+PDA+CFL+PL


Sample test
Sample Test “yes” or “no” is called an


(Nothing “useless”) “yes” or “no” is called an

Example 3.4.1 on P. 105ff M&S


End of Test! “yes” or “no” is called an


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