1. Programming Language Concepts
03/01/2019
Regular Expressions
Programming Language Concepts
Lecture 5
Prepared by
Manuel E. Bermúdez, Ph.D.
Associate Professor
University of Florida

2. Regular Expressions A compact, easy-to-read language description.
03/01/2019
Regular Expressions
A compact, easy-to-read language description.
Use operators to denote the language constructors described earlier, to build “complex” languages from simple “atomic” ones.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

3. 03/01/2019
Regular Expressions
Definition: A regular expression over an alphabet Σ is recursively defined as follows:
ø denotes language ø
ε denotes language {ε}
a denotes language {a}, for all a  Σ.
(P + Q) denotes L(P) U L(Q), where P, Q are r.e.’s.
(PQ) denotes L(P)·L(Q), where P, Q are r.e.’s.
P* denotes L(P)*, where P is r.e.
To prevent excessive parentheses, we assume left associativity, with the following operator precedence hierarchy, from most to least binding: *, ·, +
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

4. Regular Expressions Examples: (O + 1)*: any string of O’s and 1’s.
03/01/2019
Regular Expressions
Examples:
(O + 1)*: any string of O’s and 1’s.
(O + 1)*1: any string of O’s and 1’s, ending with a 1.
1*O1*: any string of 1’s with a single O inserted.
Letter (Letter + Digit)*: an identifier.
Digit Digit*: an integer.
Quote Char* Quote: a string. †
# Char* Eoln: a comment. †
{Char*}: another comment. †
† Assuming that Char does not contain quotes,
eoln’s, or } .
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

5. 03/01/2019
Regular Expressions
Conversion from Right-linear grammars to regular expressions
Example:
S → aS R → aS
→ bR
→ ε
What does S → aS mean?
L(S)  {a}·L(S)
S → bR means L(S)  {b}·L(R)
S → ε means L(S) {ε}
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

6. Regular Expressions Together, they mean that
03/01/2019
Regular Expressions
Together, they mean that
L(S) = {a}·L(S) + {b}·L(R) + {ε}
or S = aS + bR + ε
Similarly, R → aS means R = aS.
Thus, S = aS + bR + ε
R = aS
System of simultaneous equations, in which the variables are nonterminals.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

7. Regular Expressions Solving systems of simultaneously equations.
03/01/2019
Regular Expressions
Solving systems of simultaneously equations.
S = aS + bR + ε
R = aS
Back substitute R = aS:
S = aS + baS + ε
= (a + ba) S + ε
Question: What to do with equations of the form:
X = X + β ?
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

8. Regular Expressions Answer: β  L(x), so αβ  L(x), ααβ  L(x),
03/01/2019
Regular Expressions
Answer: β  L(x), so αβ  L(x),
ααβ  L(x),
αααβ  L(x), …
Thus α*β = L(x).
In our case,
S = (a + ba) S + ε
= (a + ba)* ε
= (a + ba)*
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

9. Right-linear regular grammar
03/01/2019
Regular Expressions
Right-linear regular grammar ↓
regular expression
1. A = α1 + α2 + … + αn if A → α1
→ α2 .
→ αn
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

10. 03/01/2019
Regular Expressions
If equation is of the form X = α, where X does not appear in α, then replace every occurrence of X with α in all other equations, and delete equation X = α.
If equation is of the form X = αX + β, where X does not occur in either α or β, then replace the equation with X = α*β.
Note: Some algebraic manipulations may be needed to obtain the form X = αX + β.
Important: Catenation is not commutative!!
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

11. Regular Expressions Example: S → a R → abaU U → aS → bU → U → b → bR
03/01/2019
Regular Expressions
Example:
S → a R → abaU U → aS
→ bU → U → b
→ bR
S = a + bU + bR
R = abaU + U = (aba + ε) U
U = aS + b
Back substitute R:
S = a + bU + b(aba + ε) U
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

12. Regular Expressions Back substitute U:
03/01/2019
Regular Expressions
Back substitute U:
S = a + b(aS + b) + b(aba + ε)(aS + b)
= a + baS + bb + babaaS + babab + baS + bb
= (ba + babaa)S + (a + bb + babab)
therefore
S = (ba + babaa)*(a + bb + babab)
repeats
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

13. Regular Expressions Summarizing: RGR RGL Minimum DFA RE NFA DFA Done
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Regular Expressions
Summarizing:
RGR RGL Minimum
DFA
RE NFA DFA
Done
Soon
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

14. Regular Expressions Regular Expression ↓ ALGORITHM 1 NFA
03/01/2019
Regular Expressions
Regular Expression ↓
NFA
Recursively build the FSA, mimicking the structure of the regular expression. Each FSA built has one start state, and one final state.
Conversions:
if ø
ALGORITHM 1
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. 1 2

15. Regular Expressions if ε if a if P + Q if P· Q or a ε ε ε ε ε ε ε ε 1
03/01/2019
Regular Expressions
if ε
if a
if P + Q
if P· Q or 1 a 1 2 P ε ε 1 2 ε
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. ε Q ε P Q ε ε ε 1 P Q 2

16. Regular Expressions ε if P* Example: (b (aba + ε) a)* (b (aba + ε) a)*
03/01/2019
Regular Expressions ε
if P*
Example: (b (aba + ε) a)*
(b (aba + ε) a)* ε ε 1 P 2 ε b 1 2
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. a 3 4 b 5 6

17. Regular Expressions a (b (aba + ε) a)* a a ε b 3 ε 7 a 7 8 9 10 11 4 5
03/01/2019
Regular Expressions a
(b (aba + ε) a)* 7 8 9 a 10 11 a ε b 3 4 5 6
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. ε 7 8 a

18. Regular Expressions (b (aba + ε) a)* a ε b 3 ε ε 12 9 7 ε ε ε a b ε a
03/01/2019
Regular Expressions
(b (aba + ε) a)* a ε b 3 ε 4 5 6 ε 12 9 7 ε 13 8 ε ε a b 2 1 ε a ε b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. 3 ε 4 5 6 ε 12 9 7 ε 13 8 ε ε a

19. Regular Expressions (b (aba + ε) a) * b ε a ε b ε 3 ε 12 9 7 ε ε ε a ε
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Regular Expressions
(b (aba + ε) a) * b 2 1 ε a ε b ε 3 4 5 6 ε 12 9 7 ε 13 8 ε ε a ε 10 a
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. 11

20. Regular Expressions (b (aba + ε) a)* ε b ε ε a 14 2 ε ε ε ε 11 9 5 ε a
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Regular Expressions
(b (aba + ε) a)* ε b ε ε a 14 2 1 12 3 4 ε ε ε ε 11 9 5 ε a ε 15 13 6 10 8 7 ε ε a ε
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

21. Regular Expressions Regular Expression ↓ ALGORITHM 2 NFA Start With: E
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Regular Expressions
Regular Expression ↓
NFA
Start With:
ALGORITHM 2 E
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

22. Regular Expressions Apply Rules: a a* ε ε ab a b a a + b b
03/01/2019
Regular Expressions
Apply Rules: a a* ε ε ab a b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. a
a + b b

23. Regular Expressions Algorithm 1: Builds FSA bottom up
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Regular Expressions
Algorithm 1:
Builds FSA bottom up
Good for machines
Bad for humans
Algorithm 2:
Builds FSA top down
Bad for machines
Good for humans
Arguable
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

24. Regular Expressions Example (Algorithm 2): (a + b)* (aa + bb) (a + b)*
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Regular Expressions
Example (Algorithm 2):
(a + b)* (aa + bb)
(a + b)*
aa + bb aa ε ε
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. bb
a + b a a ε ε b b a b

25. Regular Expressions Example (Algorithm 2): ba(a + b)* ab a b a ε ε a b
03/01/2019
Regular Expressions
Example (Algorithm 2):
ba(a + b)* ab a b a ε ε a b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. b

26. Regular Expressions Deterministic Finite-State Automata (DFA’s)
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Regular Expressions
Deterministic Finite-State Automata (DFA’s)
Definition: A deterministic FSA is defined just like an NFA, except that
δ: Q x Σ → Q, rather than
δ: Q x Σ U {ε}→ 2Q
Thus, both
and
are impossible.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. ε a a

27. 03/01/2019
Regular Expressions
Every transition of a DFA consumes a symbol. Fortunately, DFA’s are just as powerful as NFA’s.
Theorem: For every NFA there exists an equivalent (accepting the same language) DFA.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

28. Regular Expressions Conversion from NFA’s to DFA’s:
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Regular Expressions
Conversion from NFA’s to DFA’s:
“Simulate” all moves of the NFA with the DFA.
The start state of the DFA is the start state of the NFA (say, S), together with states that are ε-reachable from S.
Each state in the DFA is a subset of the set of states of the NFA; the notion of being in “any one of” a number of states.
New states in the DFA are constructed by calculating the sets of states that are reachable through symbols, after the start state.
The final states in the DFA are those that contain any final state of the NFA.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

29. Regular Expressions Example: a*b + ba* a ε 2 3 b ε a 6 1 NFA b ε ε 4 5
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Regular Expressions
Example: a*b + ba* a ε 2 3 b ε a 6 1
NFA b ε ε 4 5
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

30. Regular Expressions ε b 1 3 4 2 5 6 a DFA Input State a b 123 23 456
03/01/2019 ε b 1 3 4 2 5 6 a
Regular Expressions
DFA
Input
State a b
NFA
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. a b 6 23 a
DFA
123 b a a
456 56

31. 03/01/2019
Regular Expressions
In general, if NFA has N states, the DFA can have as many as 2N states.
Example: ba (a + b)* ab ε a 3 5 6 4 7 8 b 1 2 11 10 9
NFA
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

32. DFA Input State a b 0 --- 1 1 234689 --- 234689 34568910 346789
03/01/2019
DFA
Input
State a b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

33. Regular Expressions a 34568910 b a b a a 1 234689 a 34678911 b 346789
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Regular Expressions a b a b a a 1
234689 a b
346789 b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations. b

34. Regular Expressions State Minimization
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Regular Expressions
State Minimization
Theorem: Given a DFA M, there exists an equivalent DFA M’ that is minimal, i.e. no other equivalent DFA exists with fewer states than M’.
Definition: A partition of a set S is a set of subsets of S such that every element of S appears in exactly one of the subsets.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

35. Regular Expressions Example: S = {1, 2, 3, 4, 5}
03/01/2019
Regular Expressions
Example: S = {1, 2, 3, 4, 5}
Π1 = { {1, 2, 3, 4}, {5} }
Π2 = { {1, 2, 3,}, {4}, {5} }
Π3 = { {1, 3}, {2}, {4}, {5} }
Note: Π2 is a refinement of Π1 , and Π3 is a refinement of Π2.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

36. Regular Expressions Minimization Algorithm:
03/01/2019
Regular Expressions
Minimization Algorithm:
Remove all undefined transitions by introducting a TRAP state, i.e. a state from which no final state is reachable.
Partition all states into two groups (final states and non-final states).
Complete the “Next State” table for each group, by specifying transitions from group to group.
Form the next partition: split groups in which Next State table entries differ.
Repeat 3 until no further splitting is possible.
Determine start and final states.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

37. Regular Expressions a b Example: Π0 = { {1, 2, 3, 4}, {5} } State a b
03/01/2019
Regular Expressions a b
Example:
Π0 = { {1, 2, 3, 4}, {5} }
State a b a b 1 2 3 5 4 b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.
Split {4} from partition {1,2,3,4}

38. Regular Expressions a b 1 2 3 5 4 Π1 = { {1, 2, 3}, {4}, {5} }
03/01/2019
Regular Expressions a b 1 2 3 5 4
Π1 = { {1, 2, 3}, {4}, {5} }
State a b
Split {2} from partition {1,2,3}
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

39. Regular Expressions Π2 = { {1, 3}, {2}, {4}, {5} } State a b 1 2 13
03/01/2019
Regular Expressions
Π2 = { {1, 3}, {2}, {4}, {5} }
State a b
No more splitting Minimal DFA 5 13 4 2 a b
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.

40. Regular Expressions Summary of Regular Languages
03/01/2019
Regular Expressions
Summary of Regular Languages
Smallest class in the Chomsky hierarchy.
Appropriate for lexical analysis.
Four representations: RGR , RGL , RE and FSA.
All four are equivalent; there are algorithms to perform transformations among them.
Various advantages and disadvantages among these four, for language designer, implementor, and user.
FSA’s can be made deterministic, and minimal.
Be selective. You do not need to cover both research and education. It does not need to be a long list. You can put down just one opportunity that you are really excited about. Just identify what you think are the biggest opportunities for your department faculty. Strike a balance between “thinking big” and being realistic. One way to think would be to say that if you were the Dean, you would invest in these opportunities. Remember the goal is to have national level prominence and visibility where our peer group will recognize our activities and accomplishments. For example, the NSF ERC on Particle Science and Technology
As you go to the next slide, please bear in mind that there may well be very strong connections between this slide and the next on multi-disciplinary collaborations.