6 research outputs found
A complete approximation theory for weighted transition systems
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes with the weights within the same boundaries. We propose a customized modal logic that expresses these numeric boundaries for transition weights by means of particular modalities. We prove that our logic is invariant under the proposed notion of bisimulation. We show that the logic enjoys the finite model property which allows us to prove the decidability of satisfiability and provide an algorithm for satisfiability checking. Last but not least, we identify a complete axiomatization for this logic, thus solving a long-standing open problem in this field. All our results are proven for a class of WTSs without the image-finiteness restriction, a fact that makes this development general and robust
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
Continuous-time temporal logic specification and verification for nonlinear biological systems in uncertain contexts
In this thesis we introduce a complete framework for modelling and verification of biological systems in uncertain contexts based on the bond-calculus process algebra and
the LBUC spatio-temporal logic. The bond-calculus is a biological process algebra which
captures complex patterns of interaction based on affinity patterns, a novel communication
mechanism using pattern matching to express multiway interaction affinities and general
kinetic laws, whilst retaining an agent-centric modelling style for biomolecular species.
The bond-calculus is equipped with a novel continuous semantics which maps models to
systems of Ordinary Differential Equations (ODEs) in a compositional way.
We then extend the bond-calculus to handle uncertain models, featuring interval uncertainties in their species concentrations and reaction rate parameters. Our semantics is also
extended to handle uncertainty in every aspect of a model, producing non-deterministic
continuous systems whose behaviour depends either on time-independent uncertain parameters and initial conditions, corresponding to our partial knowledge of the system at
hand, or time-varying uncertain inputs, corresponding to genuine variability in a system’s
behaviour based on environmental factors.
This language is then coupled with the LBUC spatio-temporal logic which combines
Signal Temporal Logic (STL) temporal operators with an uncertain context operator
which quantifies over an uncertain context model describing the range of environments
over which a property must hold. We develop model-checking procedures for STL and
LBUC properties based on verified signal monitoring over flowpipes produced by the
Flow* verified integrator, including the technique of masking which directs monitoring for
atomic propositions to time regions relevant to the overall verification problem at hand.
This allows us to monitor many interesting nested contextual properties and frequently
reduces monitoring costs by an order of magnitude. Finally, we explore the technique
of contextual signal monitoring which can use a single Flow* flowpipe representing a
functional dependency to complete a whole tree of signals corresponding to different
uncertain contexts. This allows us to produce refined monitoring results over the whole
space and to explore the variation in system behaviour in different contexts
Concurrent weighted logic
We introduce Concurrent Weighted Logic (CWL), a multimodal logic for concurrent labeled weighted transition systems (LWSs). The synchronization of LWSs is described using dedicated functions that, in various concurrency paradigms, allow us to encode the compositionality of LWSs. To reflect these, CWL contains modal operators indexed with rational numbers to predicate over the numerical labels of LWSs as well as a binary modal operator that encodes properties concerning the (de-) composition of LWSs. We develop a Hilbert-style axiomatic system for CWL and we prove weak- and strong-completeness results for this logic. To complete these proofs we involve advanced topological techniques from Model Theory
Concurrent weighted logic
We introduce Concurrent Weighted Logic (CWL), a multimodal logic for concurrent labeled weighted transition systems (LWSs). The synchronization of LWSs is de-scribed using dedicated functions that, in various concurrency paradigms, allow us to encode the compositionality of LWSs. To reflect these, CWL contains modal operators indexed with rational numbers to predicate over the numerical labels of LWSs as well as a binary modal operator that encodes properties concerning the (de-) composition of LWSs. We develop a Hilbert-style axiomatic system for CWL and we prove weak-and strong-completeness results for this logic. To complete these proofs we involve advanced topological techniques from Model Theory