Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects

05/21/2019
by   Mathias Ruggaard Pedersen, et al.
0

Computer systems can be found everywhere: in space, in our homes, in our cars, in our pockets, and sometimes even in our own bodies. For concerns of safety, economy, and convenience, it is important that such systems work correctly. However, it is a notoriously difficult task to ensure that the software running on computers behaves correctly. One approach to ease this task is that of model checking, where a model of the system is made using some mathematical formalism. Requirements expressed in a formal language can then be verified against the model in order to give guarantees that the model satisfies the requirements. For many computer systems, time is an important factor. As such, we need our formalisms and requirement languages to be able to incorporate real time. We therefore develop formalisms and algorithms that allow us to compare and express properties about real-time systems. We first introduce a logical formalism for reasoning about upper and lower bounds on time, and study the properties of this formalism, including axiomatisation and algorithms for checking when a formula is satisfied. We then consider the question of when a system is faster than another system. We show that this is a difficult question which can not be answered in general, but we identify special cases where this question can be answered. We also show that under this notion of faster-than, a local increase in speed may lead to a global decrease in speed, and we take step towards avoiding this. Finally, we consider how to compare the real-time behaviour of systems not just qualitatively, but also quantitatively. Thus, we are interested in knowing how much one system is faster or slower than another system. This is done by introducing a distance between systems. We show how to compute this distance and that it behaves well with respect to certain properties.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

05/23/2019

Formalizing Time4sys using parametric timed automata

Critical real-time systems must be verified to avoid the risk of dramati...
07/29/2019

Time4sys2imi: A tool to formalize real-time system models under uncertainty

Time4sys is a formalism developed by Thales, realizing a graphical speci...
10/24/2017

Deadlock and Termination Detection using IMDS Formalism and Model Checking. Version 2

Modern model checking techniques concentrate on global properties of ver...
07/17/2013

Model checking coalitional games in shortage resource scenarios

Verification of multi-agents systems (MAS) has been recently studied tak...
03/11/2019

Towards Deriving Verification Properties

Formal software verification uses mathematical techniques to establish t...
05/06/2021

Algorithmic Ethics: Formalization and Verification of Autonomous Vehicle Obligations

We develop a formal framework for automatic reasoning about the obligati...
07/08/2016

From Collective Adaptive Systems to Human Centric Computation and Back: Spatial Model Checking for Medical Imaging

Recent research on formal verification for Collective Adaptive Systems (...
This week in AI

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