8 research outputs found
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
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