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E Proofs for Section 6

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This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license.

Authors:

(1) Pascal Baumann, Max Planck Institute for Software Systems (MPI-SWS), Germany;

(2) Rupak Majumdar, Max Planck Institute for Software Systems (MPI-SWS), Germany;

(3) Ramanathan S. Thinniyam, Max Planck Institute for Software Systems (MPI-SWS), Germany;

(4) Georg Zetzsche, Max Planck Institute for Software Systems (MPI-SWS), Germany.

Table of Links

Introduction

Dynamic Networks of Concurret Pushdown Systems (DCPS)

Warm-up: Non-Termination

Fair Non-Termination

From Progressive Runs for VASSB to Reachability

Starvation

Conclusion, Acknowledgment & References

A. Strengthening Fairness to Progressive Runs

B. Proofs from Section 4.1

C. Proofs for Section 5

D. Proofs for Section 5.3

E. Proofs for Section 6

E PROOFS FROM SECTION 6

E.1 Proof of Lemma 6.1

Lemma 6.1. A DCPS has a starving run if and only if it has a consistent run.


E.2 Proof of Lemma 6.4 E.3 Freezing DCPS

E.5 Proof of Lemma 6.7

In this section, we prove Lemma 6.7. It will be convenient to use a slightly modified definition of pushdown automata for this.


E.6 Proof of Lemma 6.11

E.7 Proof of Proposition 6.9

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