Concurrency Theory(WS 2016) Out: Thu, 08 Dec Due: Wed, 14 Dec
Exercise Sheet 7
D’Osualdo, Lederer, Schneider Technische Universit¨at Kaiserslautern
Problem 1: Complements of downward-closed sets
Let(Q,≤)be a qo andB ⊆Q. Show thatB↓is upward-closed.
Problem 2: Backwards search for Petri nets
a) Give an algorithm to computeminprefor Petri nets. Argue about its correctness.
b) Consider the following Petri net:
p1
p2
p3
p4
t0
t1
t2
Run the backwards search to prove that the markingM = 0 0 2 0
is coverable.
Problem 3: Backwards search for LCS
Consider the LCS depicted in the figure below.
q0 N!1 q1 q2 q3 q4
A!1 N!0
A?0
N?1 N!0
N?0
Determine if configurations(q4,
Nentry
↓
0 ε
↑
Aentry
)and(q4, ε
1
)are coverable using the known procedure.
Problem 4: Reduction of Boundedness
We call a LCSboundedif its configuration space is finite.
Reduce boundedness of reset nets to boundedness of LCS, i.e. given a reset netR, construct a LCSSRsuch thatRis bounded iffSRis bounded. Argue correctness of the construction.
