115,885 research outputs found
Structural operational semantics for stochastic and weighted transition systems
We introduce weighted GSOS, a general syntactic framework to specify well-behaved transition systems where transitions are equipped with weights coming from a commutative monoid. We prove that weighted bisimilarity is a congruence on systems defined by weighted GSOS specifications. We illustrate the flexibility of the framework by instantiating it to handle some special cases, most notably that of stochastic transition systems. Through examples we provide weighted-GSOS definitions for common stochastic operators in the literature
Structural Operational Semantics for Stochastic Process Calculi
A syntactic framework called SGSOS, for defining well-behaved Markovian stochastic transition systems, is introduced by analogy to the GSOS congruence format for nondeterministic processes. Stochastic bisimilarity is guaranteed a congruence for systems defined by SGSOS rules. Associativity of parallel composition in stochastic process algebras is also studied within the SGSOS framework
Reactive Systems over Cospans
The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we offer a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konigās rewriting via borrowed contexts and opens the way to a unified treatment of several applications
Distributive Laws and Decidable Properties of SOS Specifications
Some formats of well-behaved operational specifications, correspond to
natural transformations of certain types (for example, GSOS and coGSOS laws).
These transformations have a common generalization: distributive laws of monads
over comonads. We prove that this elegant theoretical generalization has
limited practical benefits: it does not translate to any concrete rule format
that would be complete for specifications that contain both GSOS and coGSOS
rules. This is shown for the case of labeled transition systems and
deterministic stream systems.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
Imprecise Continuous-Time Markov Chains
Continuous-time Markov chains are mathematical models that are used to
describe the state-evolution of dynamical systems under stochastic uncertainty,
and have found widespread applications in various fields. In order to make
these models computationally tractable, they rely on a number of assumptions
that may not be realistic for the domain of application; in particular, the
ability to provide exact numerical parameter assessments, and the applicability
of time-homogeneity and the eponymous Markov property. In this work, we extend
these models to imprecise continuous-time Markov chains (ICTMC's), which are a
robust generalisation that relaxes these assumptions while remaining
computationally tractable.
More technically, an ICTMC is a set of "precise" continuous-time finite-state
stochastic processes, and rather than computing expected values of functions,
we seek to compute lower expectations, which are tight lower bounds on the
expectations that correspond to such a set of "precise" models. Note that, in
contrast to e.g. Bayesian methods, all the elements of such a set are treated
on equal grounds; we do not consider a distribution over this set.
The first part of this paper develops a formalism for describing
continuous-time finite-state stochastic processes that does not require the
aforementioned simplifying assumptions. Next, this formalism is used to
characterise ICTMC's and to investigate their properties. The concept of lower
expectation is then given an alternative operator-theoretic characterisation,
by means of a lower transition operator, and the properties of this operator
are investigated as well. Finally, we use this lower transition operator to
derive tractable algorithms (with polynomial runtime complexity w.r.t. the
maximum numerical error) for computing the lower expectation of functions that
depend on the state at any finite number of time points
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
Convergence acceleration and stabilization for dynamical-mean-field-theory calculations
The convergence to the self-consistency in the dynamical-mean-field-theory
(DMFT) calculations for models of correlated electron systems can be
significantly accelerated by using an appropriate mixing of hybridization
functions which are used as the input to the impurity solver. It is shown that
the techniques and the past experience with the mixing of input charge
densities in the density-functional-theory (DFT) calculations are also
effective in DMFT. As an example, the increase of the computational
requirements near the Mott metal-insulator transition in the Hubbard model due
to critical slowing down can be strongly reduced by using the modified
Broyden's method to numerically solve the non-linear self-consistency equation.
Speed-up factors as high as 3 were observed in practical calculations even for
this relatively well behaved problem. Furthermore, the convergence can be
achieved in difficult cases where simple linear mixing is either not effective
or even leads to divergence. Unstable and metastable solutions can also be
obtained. We also determine the linear response of the system with respect to
the variations of the hybridization function, which is related to the
propagation of the information between the different energy scales during the
iteration.Comment: 9 pages, 8 figure
The Steady-State Response of a Class of Dynamical Systems to Stochastic Excitation
In this paper a class of coupled nonlinear dynamical systems subjected to stochastic excitation is considered. It is shown how the exact steady-state probability density function for this class of systems can be constructed. The result is then applied to some classical oscillator problems
- ā¦