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Erik Jonsson School of Engineering and Computer SciencePowerPoint Presentation

Erik Jonsson School of Engineering and Computer Science

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### Context-free Languages turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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

### O turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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

### Pushdown Automata turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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

### PUMPING LEMMA turned up a draft of an early unpublished paper by the famed physicist that concluded, mistakenly, that new matter, such as stars and galaxies, would appear to fill the expanding universe.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

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

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

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

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

### PRACTICE “yes” or “no” is called an

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.

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 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.

Useful variables and productions

Left-recursion

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 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

Many similar definitions

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 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

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

Martin, P. 218; H&U, P. 115 complement)!

CS 341 – UT-Austin complement)!

CS 341 – UT-Austin complement)!

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.

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”

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

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.

- 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)

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

- One’s Complement: “yes” or “no” is called an
- Increment:

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

CHAPTER_ONE

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

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

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

Parsing “yes” or “no” is called an

LL(k) Grammars

CFG+PDA+CFL+PL

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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