516 research outputs found
Enumerating Tarski fixed points on lattices of binary relations
We study the problem of enumerating Tarski fixed points, focusing on the
relational lattices of equivalences, quasiorders and binary relations. We
present a polynomial space enumeration algorithm for Tarski fixed points on
these lattices and other lattices of polynomial height. It achieves polynomial
delay when enumerating fixed points of increasing isotone maps on all three
lattices, as well as decreasing isotone maps on the lattice of binary
relations. In those cases in which the enumeration algorithm does not guarantee
polynomial delay on the three relational lattices on the other hand, we prove
exponential lower bounds for deciding the existence of three fixed points when
the isotone map is given as an oracle, and that it is NP-hard to find three or
more Tarski fixed points. More generally, we show that any deterministic or
bounded-error randomized algorithm must perform a number of queries
asymptotically at least as large as the lattice width to decide the existence
of three fixed points when the isotone map is given as an oracle. Finally, we
demonstrate that our findings yield a polynomial delay and space algorithm for
listing bisimulations and instances of some related models of behavioral or
role equivalence
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
Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
The symmetric interaction combinators are an equally expressive variant of
Lafont's interaction combinators. They are a graph-rewriting model of
deterministic computation. We define two notions of observational equivalence
for them, analogous to normal form and head normal form equivalence in the
lambda-calculus. Then, we prove a full abstraction result for each of the two
equivalences. This is obtained by interpreting nets as certain subsets of the
Cantor space, called edifices, which play the same role as Boehm trees in the
theory of the lambda-calculus
Behavioral equivalences for AbU: Verifying security and safety in distributed IoT systems
Attribute-based memory Updates ([Formula presented]in short) is an interaction mechanism recently introduced for adapting the Event-Condition-Action (ECA) programming paradigm to distributed reactive systems, such as autonomic and smart IoT device ensembles. In this model, an event (e.g., an input from a sensor, or a device state update) can trigger an ECA rule, whose execution can cause the state update of (possibly) many remote devices at once; the latter are selected āon the flyā by means of predicates over their state, without the need of a central coordinating entity. However, the combination of different [Formula presented]systems may yield unexpected interactions, e.g., when a new device is added to an existing secure system, potentially hindering the security of the whole ensemble of devices. This can be critical in the IoT, where smart devices are more and more pervasive in our daily life. In this paper, we consider the problem of ensuring security and safety requirements for [Formula presented]systems (and, in turn, for IoT devices). The first are a form of noninterference, as they correspond to avoid forbidden information flows (e.g., information flows violating confidentiality); while the second are a form of non-interaction, as they correspond to avoid unintended executions (e.g., leading to erroneous/unsafe states). In order to formally model these requirements, we introduce suitable behavioral equivalences for [Formula presented]. These equivalences are generalizations of hiding bisimilarity, i.e., a kind of weak bisimilarity where we can compare systems up to actions at different levels of security. Leveraging these behavioral equivalences, we propose (syntactic) sufficient conditions guaranteeing the requirements and, then, effective algorithms for statically verifying such conditions
Increasing Interdependence of Multivariate Distributions
Orderings of interdependence among random variables are useful in many economic contexts, for example, in assessing ex post inequality under uncertainty; in comparing multidimensional inequality; in valuing portfolios of assets or insurance policies; and in assessing systemic risk. We explore five orderings of interdependence for multivariate distributions: greater weak association, the supermodular ordering, the convex-modular ordering, the dispersion ordering, and the concordance ordering. For two dimensions, all five orderings are equivalent, whereas for an arbitrary number of dimensions n > 2, the five orderings are strictly ranked. For the special case of binary random variables, we establish some equivalences among the orderings.dependence ordering; stochastic orders; supermodularity; weak association; concordance JEL Classification Numbers: D63, D81, G11, G22
Coalgebraic Behavioral Metrics
We study different behavioral metrics, such as those arising from both
branching and linear-time semantics, in a coalgebraic setting. Given a
coalgebra for a functor , we define a framework for deriving pseudometrics on which
measure the behavioral distance of states.
A crucial step is the lifting of the functor on to a
functor on the category 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.
If has a final coalgebra, every lifting yields in a
canonical way a behavioral distance which is usually branching-time, i.e., it
generalizes bisimilarity. In order to model linear-time metrics (generalizing
trace equivalences), we show sufficient conditions for lifting distributive
laws and monads. These results enable us to employ the generalized powerset
construction
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