Download presentation

Presentation is loading. Please wait.

Published bySierra Howen Modified over 2 years ago

1
Effect of Fairness in Model Checking of Self-stabilizing programs Jingshu Chen, Fuad Abujarad and Sandeep Kulkarni

3
Problem Statement Related work Our approach Results Summary

4
To verify self-stabilizing programs by symbolic model checking stabilization: – ability of a system to converge in finite number of steps from arbitrary states to desired state. – complex algorithm Symbolic model checking: doesn’t require the designer to have considerable experience in logic reasoning.

5
Two actions: x0= xn -> x0=(x0+1) mod K xi!=xi-1 ->xi=x(i-1) Note that: the domain of x is [0,..,K-1] This program is known to be self- stabilizing if K>N. In subsequent discussion, we let K=N+1. p0p0 p1p1 p2p2 p3p3 pnpn pn-1 pipi x0 xn xi xi-1 pi-1

6
Legal state: For Process 0 either x[0]=x[n] or x[0]=(x[n]+1) mod K For i=1.. N, either x[i-1]=x[i] or x[i-1]=x[i]+1 p0p0 p1p1 p2p2 p3p3 pnpn pn-1 pipi x0 xn xi xi-1 pi-1

7
T’s work has demonstrate feasibility of applying symbolic model checking for verifying self-stabilizing programs. The result shows that verification is feasible only for programs with a small number of process.

8
Observation: - the current approach is done under weak fairness computation; - current model checker focus on weak fairness in representation of fairness. Our approach is to verify self-stabilization under unfair computation.

9
Verification under weak fairness Two actions: x0= xn -> x0=(x0+1) mod K xi!=xi-1->xi=x(i-1)

10
Verification under unfair computation

11
Verification Results for the K-state Program(execution time(s)) K=3K=4K=5K=6K=7K=8K=9K=10K=50 Unfair 00000.020.030.050.083466.3 Weakly-fair (1) 00.030.635.3334.3139.11276.1N/A Weakly-fair(2) 0.10.44.643.5285.21836N/A Approximate state space 10^110^210^310^410^510^710^810^1010^84 In spite of the improved hardware, the ability to verify self-stabilizing programs under weak fairness remains essentially the same. Scalability of verifying self-stabilization can be significantly improved for the case where the program is correct self-stabilizing without fairness.

12
For the case where weak fairness is essential for self-stabilization, – Decomposition – Utilizing the weak version of stabilization-weak stabilization

13
Verification results for Huang’s Mutual Exclusion Program n=3n=5n=7n=11n=23n=29n=31 Unfair(le)000.050.4847.12271.05704.48 Unfair(t)000.020.1514.5770.18103.8 Unfair(total)000.070.6361.69341.23808.28 Weak(le)04.15N/A Weak(t)00.63----- Weak(total)04.79N/A unfair Not Self-stabilization under this model Weak0.17N/A Approximate state space 10^410^1010^1710^3410^9310^12710^138

14
Verification Results for the K-state Program(execution time(s)) K=3K=4K=5K=6K=7K=8K=9K=10K=50 Weak stabilization 00000.020.030.050.083485.27 Weakly-fair (1) 00.030.635.3334.3139.11276.1N/A Weakly-fair(2) 0.10.44.643.5285.21836N/A Approximate state space 10^110^210^310^410^510^710^810^1010^84 Verification of weak stabilization is substantially more scalable. This result also validates the suggestion in Gouda’s work that weak stabilization is easier to verify than self-stabilization.

15
If self-stabilization is possible without fairness then cost of verifying self-stabilization is substantially lower. This is the first paper that has shown feasibility of verifying the typical self-stabilizing programs, e.g., K-state program, with large number of processes. We also identify two approaches for those cases where weak fairness is essential for self- stabilization.

Similar presentations

Presentation is loading. Please wait....

OK

INTRODUCTION TO PROGRAMMING

INTRODUCTION TO PROGRAMMING

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on professional ethics for teachers in india Ppt on search engine marketing Ppt on product data management Ppt on accounting standards 1 Ppt on synthesis and degradation of purines and pyrimidines are Ppt on review of literature example Ppt on special types of chromosomes male Ppt on unemployment in india Ppt on as 14 amalgamation process Ppt on different types of dance forms renaissance