9 research outputs found
Timed Comparisons of Semi-Markov Processes
Semi-Markov processes are Markovian processes in which the firing time of the
transitions is modelled by probabilistic distributions over positive reals
interpreted as the probability of firing a transition at a certain moment in
time. In this paper we consider the trace-based semantics of semi-Markov
processes, and investigate the question of how to compare two semi-Markov
processes with respect to their time-dependent behaviour. To this end, we
introduce the relation of being "faster than" between processes and study its
algorithmic complexity. Through a connection to probabilistic automata we
obtain hardness results showing in particular that this relation is
undecidable. However, we present an additive approximation algorithm for a
time-bounded variant of the faster-than problem over semi-Markov processes with
slow residence-time functions, and a coNP algorithm for the exact faster-than
problem over unambiguous semi-Markov processes
A Faster-Than Relation for Semi-Markov Decision Processes
When modeling concurrent or cyber-physical systems, non-functional
requirements such as time are important to consider. In order to improve the
timing aspects of a model, it is necessary to have some notion of what it means
for a process to be faster than another, which can guide the stepwise
refinement of the model. To this end we study a faster-than relation for
semi-Markov decision processes and compare it to standard notions for relating
systems. We consider the compositional aspects of this relation, and show that
the faster-than relation is not a precongruence with respect to parallel
composition, hence giving rise to so-called parallel timing anomalies. We take
the first steps toward understanding this problem by identifying decidable
conditions sufficient to avoid parallel timing anomalies in the absence of
non-determinism.Comment: In Proceedings QAPL 2019, arXiv:2001.0616
Non-Interference with What-Declassification in Component-Based Systems
Component-based design is a method for modular design of systems. The structure of component-based systems follows specific rules and single components make assumptions on the environment that they run in. In this paper, we provide a noninterference property for component-based systems that allows for a precise specification of what-declassification of information and takes assumptions on the environment into consideration in order to allow a modular, precise and re-usable information-flow analysis. For precise analysis, components can be analyzed by separately analysing services provided by a component, and from our compositionality theorem non-interference of components follows
Behavioural Preorders on Stochastic Systems - Logical, Topological, and Computational Aspects
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.Comment: PhD dissertation from Aalborg Universit