Checking Qualitative Liveness Properties of Replicated Systems with Stochastic Scheduling

05/07/2020
by   Michael Blondin, et al.
0

We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

07/15/2020

Peregrine 2.0: Explaining Correctness of Population Protocols through Stage Graphs

We present a new version of Peregrine, the tool for the analysis and par...
05/16/2020

Distributed Bounded Model Checking

Program verification is a resource-hungry task. This paper looks at the ...
02/19/2018

Reduced Dependency Spaces for Existential Parameterised Boolean Equation Systems

A parameterised Boolean equation system (PBES) is a set of equations tha...
09/30/2011

Causes of Ineradicable Spurious Predictions in Qualitative Simulation

It was recently proved that a sound and complete qualitative simulator d...
11/04/2019

Controlling a random population

Bertrand et al. introduced a model of parameterised systems, where each ...
02/06/2018

Deciding Detectability for Labeled Petri Nets

Detectability of discrete event systems (DESs) is a property to determin...
11/12/2017

Ensuring Liveness Properties of Distributed Systems (A Research Agenda)

Often fairness assumptions need to be made in order to establish livenes...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.