Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
Tarskis Fixedpoint Lemma
Recall:
We identify a predicate with the set of states in which the predicate is true.
Predicates are ordered via set inclusion.
X is a xed point of i (X) = X.
A predicate transformer is monotonic i P Q implies (P ) (Q).
A p
Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
Lecture 4: Symbolic Model Checking with BDDs
Edmund M. Clarke, Jr.
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA 15213
Temporal Logic Model Checking
Specication Language: A propositional temporal logic.
Verication Procedure: Exhaus
Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
15414
HW 4
1
Instructor: Edmund M. Clarke
TAs: Soonho Kong, David Henriques
Due date: 10/26/2011
cmu15414ta@gmail.com
Assignment 4
1
Monotonicity, Continuity, and Fixed Points
(a) Show that a monotonic function : P(S) P(S) is
continuous if S is a nite s
Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
15414
HW 3
1
Instructors: Edmund M. Clarke, Sagar Chaki, Arie Gurnkel
TAs: Soonho Kong, David Henriques
Due date: 10/05/2011
cmu15414ta@gmail.com
Assignment 3
Problem 1
Consider the Boolean formula f :
(x1 x2 x3 ) (x2 x4 ) (x3 x4 )
Part 1. One possible v
Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
Model Checking with the
Partial Order Reduction
Edmund M. Clarke, Jr.
Computer Science Department
Carnegie Mellon University
Pittsburgh, PA 15213
1
Asynchronous Computation
The interleaving model for asynchronous systems allows
concurrent events to be ord
Bug Catching: Automated Program Verification and Testing
CS 15414

Fall 2011
15414
HW 1
1
Instructor: Edmund M. Clarke
TAs: Soonho Kong, David Henriques
Due date: 09/14/2011
cmu15414ta@gmail.com
Assignment 1
1
Truth Tables
For each of the pairs of formulae below, construct a truth table that shows if the two formulae are
equivale