1. CS154 Formal Languages and Computability Thaddeus Aid Department of Computer Science San Jose State University Spring 2016 Creative Commons Attribution-ShareAlike 4.0 International License 1

2. Apple and the FBI The Fourth Amendment of the U.S. Constitution provides, "[t]he right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.“ San Bernardino Shooting - December 2, 2015, 14 people were killed and 22 were seriously injured. The FBI recovered an encrypted cell phone belonging to the shooter. Creative Commons Attribution-ShareAlike 4.0 International License 2

3. Apple and the FBI (cont.) The FBI has a valid reason for wanting to get into the phone. Owned by a domestic terrorist and could contain information to stop future shootings. The FBI does not have the technical capability to hack the phone. Well known bias against counter culture hackers and “criminals” Apple made the phone Apple has spent years improving the security on the iPhone in order to protect users, businesses, and the government. The FBI wants Apple to create a backdoor into the iPhone. Creative Commons Attribution-ShareAlike 4.0 International License 3

4. Apple and the FBI (cont) A Judge has issued a warrant to tell Apple to cooperate. What does that mean? Apple is being forced to create a tool that will break their own encryption. This will be a “master key”, you have to defeat the algorithm. Once it is invented it cannot be uninvented. Hackers are really good at getting things they want. It will be a matter of time before the master key is released into the wild. Creative Commons Attribution-ShareAlike 4.0 International License 4

5. Apple and the FBI Apple is refusing. CEO is willing to take it to the Supreme Court What does this mean for the rest of us. Security vs Privacy? Ecommerce? Creative Commons Attribution-ShareAlike 4.0 International License 5

6. Citation Lecture developed in conjunction with: Introduction to Theory of Computation Anil Maheshwari Michiel Smid http://cglab.ca/~michiel/TheoryOfComputation/TheoryOfComputation.pdf Creative Commons Attribution-ShareAlike 4.0 International License 6

7. Finite Automata - Review DFA – 5-tuple Creative Commons Attribution-ShareAlike 4.0 International License 7

8. Finite Automata - Review Non-deterministic Finite Automata Adds ε-transitions to the DFA in order to get different results from the same input. For any NFA there exists a more complicated DFA. Creative Commons Attribution-ShareAlike 4.0 International License 8

9. Closure Closure is a concept that often comes up when discussion sets of things. Closure is the idea that you can take some member of a set Change it by doing [some operation] to it Because the set is closed under [some operation] The new thing must still be in the set. Source: http://cseweb.ucsd.edu/~clbailey/ClosureOverview.htmhttp://cseweb.ucsd.edu/~clbailey/ClosureOverview.htm Creative Commons Attribution-ShareAlike 4.0 International License 9

10. Closure Example The set “Candy” The set Candy contains all individual pieces of candy. If you take a piece of candy, and drop it on the ground, is it still candy? According to the 5-second rule, I would still eat it, so it's still candy. That means that our set Candy is closed under the operation "drop.“ What if I take two pieces of candy, x and y, and stick them together? stick(x,y)--to make a new piece of candy. Since what comes out of stick(x.y) is a piece of candy, Candy is closed under stick. Note: it only works if both operands are candy. Source: http://cseweb.ucsd.edu/~clbailey/ClosureOverview.htmhttp://cseweb.ucsd.edu/~clbailey/ClosureOverview.htm Creative Commons Attribution-ShareAlike 4.0 International License 10

11. Closure Example (Cont.) I take a piece of candy, x, and feed it to a bird. Then later, after digesting the candy, the bird leaves some droppings on my car Assume the droppings came from the candy, and we'll call this bird(x) Is bird(x) candy? No way. So Candy is not closed under bird. Source: http://cseweb.ucsd.edu/~clbailey/ClosureOverview.htmhttp://cseweb.ucsd.edu/~clbailey/ClosureOverview.htm Creative Commons Attribution-ShareAlike 4.0 International License 11

12. Closure Example (Final) An important part of closure is that when we say that the set is "closed under" an operation. It has to be true for everything in the set. So even if all kinds of candies--except for one--were still candy after the bird() operation. Candy would still not be closed under bird(). Source: http://cseweb.ucsd.edu/~clbailey/ClosureOverview.htmhttp://cseweb.ucsd.edu/~clbailey/ClosureOverview.htm Creative Commons Attribution-ShareAlike 4.0 International License 12

13. Closed Operators Creative Commons Attribution-ShareAlike 4.0 International License 13

14. Regular Expressions - Review Creative Commons Attribution-ShareAlike 4.0 International License 14

15. Regular Expressions – Review (Cont) Creative Commons Attribution-ShareAlike 4.0 International License 15

16. Languages - Review Creative Commons Attribution-ShareAlike 4.0 International License 16

17. Regular Expression Identities Creative Commons Attribution-ShareAlike 4.0 International License 17

18. Regular Expression Identities Creative Commons Attribution-ShareAlike 4.0 International License 18

19. The Equivalence of Regular Expressions and Languages Let L be a language. Then L is regular if and only if there exists a regular expression that describes L. Creative Commons Attribution-ShareAlike 4.0 International License 19

20. Converting a DFA to a Regular Expression To the board! Creative Commons Attribution-ShareAlike 4.0 International License 20