The final is on Monday, December 18th, from 11:00 – 14:00 in TMCB 120. One page of notes allowed (any size and any font). It consists short answer problems. Here is a comprehensive list of topics:

- Create Kripke structures that satisfy temporal logic formulas (Homework 7)
- Write temporal logic formulas for specification expressed in english–be sure you know both CTL and LTL sub-logics (Homework 7)
- Prove (or disprove) if two temporal logic formulas are equivalent (Homework 8).
- Given a Kripke structure and a set of CTL formulas, determine which states are labeled with which formulas (Homework 10).
- Play computer and show how BDDs are created and managed with the
**ITE**method given a program using the Cudd interface. Be sure to show the unique table*and*the recursive trees tracking the**ITE**calls (Homework 11 and Homework 12). - Create a Boolean expression for a transition relation from a simple PROMELA program (Homework 13)
- Write a Boolean function describing the initial state of a system and perform forward reachable analysis using that function and a given transition relation (Homework 13 but doing it abstractly similar to class rather than with BDDs).
- Perform CTL model checking using Boolean functions and fix-point computations on a given Kripke structure. Show each iteration of the fix-point calculations (abstractly similar to class rather than with BDDs).

I expect the test to take 2 hours of student time.

One page of notes is allowed for the exam. You are responsible for knowing the testing center hours: double check the schedule for Saturday! Below is a comprehensive list of topics on the exam. Please note that some of the topics were not covered directly by the homework, so you will want to perhaps work a few problems on your own to prepare.

- Translate if-statements and while-statements into PROMELA
- Create a PROMELA verification model to solve a problem that uses shared memory for coordinating processes
- Create a PROMELA verification model to solve a problem that uses message passing for coordinating processes. Be familiar with all the different forms of interacting with a channel including the ability to poll, insert sorted, pattern match (including the
*eval()*function), and copy values from the channel. - Write safety properties and create traces that violate the property.
- Write liveness properties and create traces that violate the property.
- Convert a state transition system into a Buchi Automaton
- Given a Buchi Automaton, write a regular expression that includes the $\omega$-operator that is the language detected by the Automaton.
- Compute the intersection of two Buchi automaton.
- Perform double-depth-first search to detect cycles in a given Buchi automaton. Indicate pre-order traversal numbers on both searches and show the evolution of the runtime stack.
- Given a correctness property, write a never claim to detect when the property is violated.

I expect the test to take at least 1.5 hour of student time. The total time limit on the test is 2 hours.