931 research outputs found
Forward and Backward Bisimulations for Chemical Reaction Networks
We present two quantitative behavioral equivalences over species of a
chemical reaction network (CRN) with semantics based on ordinary differential
equations. Forward CRN bisimulation identifies a partition where each
equivalence class represents the exact sum of the concentrations of the species
belonging to that class. Backward CRN bisimulation relates species that have
the identical solutions at all time points when starting from the same initial
conditions. Both notions can be checked using only CRN syntactical information,
i.e., by inspection of the set of reactions. We provide a unified algorithm
that computes the coarsest refinement up to our bisimulations in polynomial
time. Further, we give algorithms to compute quotient CRNs induced by a
bisimulation. As an application, we find significant reductions in a number of
models of biological processes from the literature. In two cases we allow the
analysis of benchmark models which would be otherwise intractable due to their
memory requirements.Comment: Extended version of the CONCUR 2015 pape
Sigref ā A Symbolic Bisimulation Tool Box
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.
We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center āAutomatic Verification and Analysis of Complex Systemsā (SFB/TR 14 AVACS). See www.avacs.org for more information
Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs
Verification of PCTL properties of MDPs with convex uncertainties has been
investigated recently by Puggelli et al. However, model checking algorithms
typically suffer from state space explosion. In this paper, we address
probabilistic bisimulation to reduce the size of such an MDPs while preserving
PCTL properties it satisfies. We discuss different interpretations of
uncertainty in the models which are studied in the literature and that result
in two different definitions of bisimulations. We give algorithms to compute
the quotients of these bisimulations in time polynomial in the size of the
model and exponential in the uncertain branching. Finally, we show by a case
study that large models in practice can have small branching and that a
substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784
Language-based Abstractions for Dynamical Systems
Ordinary differential equations (ODEs) are the primary means to modelling
dynamical systems in many natural and engineering sciences. The number of
equations required to describe a system with high heterogeneity limits our
capability of effectively performing analyses. This has motivated a large body
of research, across many disciplines, into abstraction techniques that provide
smaller ODE systems while preserving the original dynamics in some appropriate
sense. In this paper we give an overview of a recently proposed
computer-science perspective to this problem, where ODE reduction is recast to
finding an appropriate equivalence relation over ODE variables, akin to
classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366
The Glory of the Past and Geometrical Concurrency
This paper contributes to the general understanding of the geometrical model
of concurrency that was named higher dimensional automata (HDAs) by Pratt. In
particular we investigate modal logics for such models and their expressive
power in terms of the bisimulation that can be captured. The geometric model of
concurrency is interesting from two main reasons: its generality and
expressiveness, and the natural way in which autoconcurrency and action
refinement are captured. Logics for this model, though, are not well
investigated, where a simple, yet adequate, modal logic over HDAs was only
recently introduced. As this modal logic, with two existential modalities,
during and after, captures only split bisimulation, which is rather low in the
spectrum of van Glabbeek and Vaandrager, the immediate question was what small
extension of this logic could capture the more fine-grained hereditary history
preserving bisimulation (hh)? In response, the work in this paper provides
several insights. One is the fact that the geometrical aspect of HDAs makes it
possible to use for capturing the hh-bisimulation, a standard modal logic that
does not employ event variables, opposed to the two logics (over less
expressive models) that we compare with. The logic that we investigate here
uses standard past modalities and extends the previously introduced logic
(called HDML) that had only forward, action-labelled, modalities. Besides, we
try to understand better the above issues by introducing a related model that
we call ST-configuration structures, which extend the configuration structures
of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and
prove the earlier results in the light of this new model. These offer a
different view on why the past modalities and geometrical concurrency capture
the hereditary history preserving bisimulation. Additional correlating insights
are also gained.Comment: 17 pages, 7 figure
Challenges in Quantitative Abstractions for Collective Adaptive Systems
Like with most large-scale systems, the evaluation of quantitative properties
of collective adaptive systems is an important issue that crosscuts all its
development stages, from design (in the case of engineered systems) to runtime
monitoring and control. Unfortunately it is a difficult problem to tackle in
general, due to the typically high computational cost involved in the analysis.
This calls for the development of appropriate quantitative abstraction
techniques that preserve most of the system's dynamical behaviour using a more
compact representation. This paper focuses on models based on ordinary
differential equations and reviews recent results where abstraction is achieved
by aggregation of variables, reflecting on the shortcomings in the state of the
art and setting out challenges for future research.Comment: In Proceedings FORECAST 2016, arXiv:1607.0200
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
Reverse Bisimulations on Stable Configuration Structures
The relationships between various equivalences on configuration structures,
including interleaving bisimulation (IB), step bisimulation (SB) and hereditary
history-preserving (HH) bisimulation, have been investigated by van Glabbeek
and Goltz (and later Fecher). Since HH bisimulation may be characterised by the
use of reverse as well as forward transitions, it is of interest to investigate
forms of IB and SB where both forward and reverse transitions are allowed. We
give various characterisations of reverse SB, showing that forward steps do not
add extra power. We strengthen Bednarczyk's result that, in the absence of
auto-concurrency, reverse IB is as strong as HH bisimulation, by showing that
we need only exclude auto-concurrent events at the same depth in the
configuration
A coalgebraic semantics for causality in Petri nets
In this paper we revisit some pioneering efforts to equip Petri nets with
compact operational models for expressing causality. The models we propose have
a bisimilarity relation and a minimal representative for each equivalence
class, and they can be fully explained as coalgebras on a presheaf category on
an index category of partial orders. First, we provide a set-theoretic model in
the form of a a causal case graph, that is a labeled transition system where
states and transitions represent markings and firings of the net, respectively,
and are equipped with causal information. Most importantly, each state has a
poset representing causal dependencies among past events. Our first result
shows the correspondence with behavior structure semantics as proposed by
Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and
have infinitely many states, but we show how they can be refined to get an
equivalent finitely-branching model. In it, states are equipped with
symmetries, which are essential for the existence of a minimal, often
finite-state, model. The next step is constructing a coalgebraic model. We
exploit the fact that events can be represented as names, and event generation
as name generation. Thus we can apply the Fiore-Turi framework: we model causal
relations as a suitable category of posets with action labels, and generation
of new events with causal dependencies as an endofunctor on this category. Then
we define a well-behaved category of coalgebras. Our coalgebraic model is still
infinite-state, but we exploit the equivalence between coalgebras over a class
of presheaves and History Dependent automata to derive a compact
representation, which is equivalent to our set-theoretical compact model.
Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin
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