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Argue whether Rackoff’s result can be used to derive an upper bound for deciding boundedness.

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Concurrency Theory (SS 2015) Out: Wed, Apr 29 Due: Tue, May 5

Exercise Sheet 2

Prof. Roland Meyer, Florian Furbach Technische Universit¨at Kaiserslautern

Problem 1: Boundedness

Argue whether Rackoff’s result can be used to derive an upper bound for deciding boundedness.

Hint: The results about boundedness from our lectures last week are useful.

Problem 2: Coverability

Give an upper bound for the complexity of deciding coverability in a safe Petri net.

Hint: Savitch’s Theorem also applies to lower space complexity classes.

Problem 3: Petri Net Program Semantics

Define a translation from a Petri net program to an equivalent Petri net. Give an upper bound for the size of the resulting Petri net.

Problem 4: Rackoff

Given the Petri net below and a marking M

2

= (1, 0, 10, 100)

T

, calculate the values of n(3, (1, 0, 0, 0)

T

) as well as f (3) and argue why the are correct.

p

1

x

p

2

c a

b

p

3

p

4

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