7 research outputs found
Compositional bisimulation metric reasoning with Probabilistic Process Calculi
We study which standard operators of probabilistic process calculi allow for
compositional reasoning with respect to bisimulation metric semantics. We argue
that uniform continuity (generalizing the earlier proposed property of
non-expansiveness) captures the essential nature of compositional reasoning and
allows now also to reason compositionally about recursive processes. We
characterize the distance between probabilistic processes composed by standard
process algebra operators. Combining these results, we demonstrate how
compositional reasoning about systems specified by continuous process algebra
operators allows for metric assume-guarantee like performance validation
Equational Reasonings in Wireless Network Gossip Protocols
Gossip protocols have been proposed as a robust and efficient method for
disseminating information throughout large-scale networks. In this paper, we
propose a compositional analysis technique to study formal probabilistic models
of gossip protocols expressed in a simple probabilistic timed process calculus
for wireless sensor networks. We equip the calculus with a simulation theory to
compare probabilistic protocols that have similar behaviour up to a certain
tolerance. The theory is used to prove a number of algebraic laws which
revealed to be very effective to estimate the performances of gossip networks,
with and without communication collisions, and randomised gossip networks. Our
simulation theory is an asymmetric variant of the weak bisimulation metric that
maintains most of the properties of the original definition. However, our
asymmetric version is particularly suitable to reason on protocols in which the
systems under consideration are not approximately equivalent, as in the case of
gossip protocols
Unwinding biological systems
Unwinding conditions have been fruitfully exploited in Information Flow Security to define persistent security properties. In this paper we investigate their meaning and possible uses in the analysis of biological systems. In particular, we elaborate on the notion of robustness and propose some instances of unwinding over the process algebra Bio-PEPA and over hybrid automata. We exploit such instances to analyse two case-studies: Neurospora crassa circadian system and Influenza kinetics models
Behavioral Metrics via Functor Lifting
We study behavioral metrics in an abstract coalgebraic setting. Given a
coalgebra alpha: X -> FX in Set, where the functor F specifies the branching
type, we define a framework for deriving pseudometrics on X which measure the
behavioral distance of states.
A first crucial step is the lifting of the functor F on Set to a functor in
the category PMet of pseudometric spaces. We present two different approaches
which can be viewed as generalizations of the Kantorovich and Wasserstein
pseudometrics for probability measures. We show that the pseudometrics provided
by the two approaches coincide on several natural examples, but in general they
differ.
Then a final coalgebra for F in Set can be endowed with a behavioral distance
resulting as the smallest solution of a fixed-point equation, yielding the
final coalgebra in PMet. The same technique, applied to an arbitrary coalgebra
alpha: X -> FX in Set, provides the behavioral distance on X. Under some
constraints we can prove that two states are at distance 0 if and only if they
are behaviorally equivalent.Comment: to be published in: Proceedings of FSTTCS 201
Compositionality of Approximate Bisimulation for Probabilistic Systems
Probabilistic transition system specifications using the rule format
ntmuft-ntmuxt provide structural operational semantics for Segala-type systems
and guarantee that probabilistic bisimilarity is a congruence. Probabilistic
bisimilarity is for many applications too sensitive to the exact probabilities
of transitions. Approximate bisimulation provides a robust semantics that is
stable with respect to implementation and measurement errors of probabilistic
behavior. We provide a general method to quantify how much a process combinator
expands the approximate bisimulation distance. As a direct application we
derive an appropriate rule format that guarantees compositionality with respect
to approximate bisimilarity. Moreover, we describe how specification formats
for non-standard compositionality requirements may be derived.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690