Model Checking Assignment 2
Exercise 1. The weak until operator W has similar semantics to the strong until
operator U except that g1 W g2 doesnt require g2 to ever hold true if g1 is globally true:
|= g1 W g2
for all j 0, if j |= g1 then there exists a
Graph-Based Algorithms
for Boolean Function Manipulation12
Randal E. Bryant3
Abstract
In this paper we present a new data structure for representing Boolean functions and an associated set of
manipulation algorithms. Functions are represented by directed,
Lecture1: 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: Exhaust
Using Cadence SMV
to verify temporal properties
of finite-state machines
1
Review of Temporal Logic
a
Xa
Fa
Ga
aUb
a is true now
a is true in the neXt state
a will be true sometime in the Future
a will be Globally true in the future
a will hold true U
Lecture 2: Symbolic Model Checking With SAT
Edmund M. Clarke, Jr.
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
(Joint work over several years with: A. Biere, A. Cimatti, Y. Zhu,
A. Gupta, J. Kukula, D. Kroening, O. Strichman)
15-817: Assignment 2
Part A. Binary Decision Diagrams. In this assignment, the word BDD, unless otherwise indicated, is to be understood as referring to a reduced, ordered binary decision diagram.
1. Draw a BDD for the formula XOR(x2 , x1 ), where XOR is
15-817: Assignment 1
Please do Parts 1 and 2 ASAP!
Part 1. Sign up for the course mailing list. Email the TA (wkleber @ cs.cmu.edu) with
i
[15-817] Subscribe YourEmailAddress as the subject line; leave the body blank. If
there are corrections or claricati
Model Checking IV
Symbolic Model Checking
Edmund M. Clarke, Jr.
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
Breakthrough!
Ken McMillan implemented a version of the CTL model checking
algorithm using OBDDs in the fall of 1987
Model Checking I
Binary Decision Diagrams
Edmund M. Clarke, Jr.
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
1/42
Binary Decision Diagrams
Ordered binary decision diagrams (OBDDs) are a canonical form for
boolean formulas.
OB
Model Checking VI
Linear-Time Temporal Logic
Edmund M. Clarke, Jr.
School of Computer Science
Carnegie Mellon University
Pittsburgh, PA 15213
Model Checking for LTL
Reduction of LTL model checking to CTL model checking with
fairness constraints
Symbolic L
15-817 Assignment 1
def
Exercise 1. Warm Up. Let f (x, y, z) = y + z x + z y + y x be a boolean formula.
Compute f s Shannon expansion with respect to
(a) x
(b) y
(c) z
Exercise 2.
x
1
1
1
1
0
0
0
0
Reduced OBDDs. Given the truth table
y z f (x, y, z)
1 1
Model Checking Assignment 3a (Due Oct 15)
Recall:
We identify a predicate with the set of states in which the predicate is true.
X is a xed point of i [X] = X.
is monotonic i P Q implies [P ] [Q].
is -continuous i P1 P2 . . . implies [i Pi ] = i [Pi ].
Model Checking Assignment 3b
Due Oct 22
Recall:
We identify a predicate with the set of states in which the predicate is true.
X is a xed point of i [X] = X.
A predicate transformer is monotonic i P Q implies [P ] [Q].
A predicate transformer is -cont
The Birth of
Model Checking
Edmund M. Clarke
Department of Computer Science
Carnegie Mellon University
Quote For The Day
When the time is ripe for certain things,
these things appear in different places in
the manner of violets coming to light in
early sp