81 research outputs found
A uniform framework for modelling nondeterministic, probabilistic, stochastic, or mixed processes and their behavioral equivalences
Labeled transition systems are typically used as behavioral models of concurrent processes, and the labeled transitions define the a one-step state-to-state reachability relation. This model can be made generalized by modifying the transition relation to associate a state reachability distribution, rather than a single target state, with any pair of source state and transition label. The state reachability distribution becomes a function mapping each possible target state to a value that expresses the degree of one-step reachability of that state. Values are taken from a preordered set equipped with a minimum that denotes unreachability. By selecting suitable preordered sets, the resulting model, called ULTraS from Uniform Labeled Transition System, can be specialized to capture well-known models of fully nondeterministic processes (LTS), fully
probabilistic processes (ADTMC), fully stochastic processes (ACTMC), and of nondeterministic and probabilistic (MDP) or nondeterministic and stochastic (CTMDP) processes. This uniform treatment of different behavioral models extends to behavioral equivalences. These can be defined on ULTraS by relying on appropriate measure functions that expresses the degree of reachability of a set of states when performing
single-step or multi-step computations. It is shown that the specializations of bisimulation, trace, and testing
equivalences for the different classes of ULTraS coincide with the behavioral equivalences defined in the literature over traditional models
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages
Labeled state-to-function transition systems, FuTS for short, admit multiple
transition schemes from states to functions of finite support over general
semirings. As such they constitute a convenient modeling instrument to deal
with stochastic process languages. In this paper, the notion of bisimulation
induced by a FuTS is proposed and a correspondence result is proven stating
that FuTS-bisimulation coincides with the behavioral equivalence of the
associated functor. As generic examples, the concrete existing equivalences for
the core of the process algebras ACP, PEPA and IMC are related to the
bisimulation of specific FuTS, providing via the correspondence result
coalgebraic justification of the equivalences of these calculi.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Weak Markovian Bisimulation Congruences and Exact CTMC-Level Aggregations for Concurrent Processes
We have recently defined a weak Markovian bisimulation equivalence in an
integrated-time setting, which reduces sequences of exponentially timed
internal actions to individual exponentially timed internal actions having the
same average duration and execution probability as the corresponding sequences.
This weak Markovian bisimulation equivalence is a congruence for sequential
processes with abstraction and turns out to induce an exact CTMC-level
aggregation at steady state for all the considered processes. However, it is
not a congruence with respect to parallel composition. In this paper, we show
how to generalize the equivalence in a way that a reasonable tradeoff among
abstraction, compositionality, and exactness is achieved for concurrent
processes. We will see that, by enhancing the abstraction capability in the
presence of concurrent computations, it is possible to retrieve the congruence
property with respect to parallel composition, with the resulting CTMC-level
aggregation being exact at steady state only for a certain subset of the
considered processes.Comment: In Proceedings QAPL 2012, arXiv:1207.055
A Definition Scheme for Quantitative Bisimulation
FuTS, state-to-function transition systems are generalizations of labeled
transition systems and of familiar notions of quantitative semantical models as
continuous-time Markov chains, interactive Markov chains, and Markov automata.
A general scheme for the definition of a notion of strong bisimulation
associated with a FuTS is proposed. It is shown that this notion of
bisimulation for a FuTS coincides with the coalgebraic notion of behavioral
equivalence associated to the functor on Set given by the type of the FuTS. For
a series of concrete quantitative semantical models the notion of bisimulation
as reported in the literature is proven to coincide with the notion of
quantitative bisimulation obtained from the scheme. The comparison includes
models with orthogonal behaviour, like interactive Markov chains, and with
multiple levels of behavior, like Markov automata. As a consequence of the
general result relating FuTS bisimulation and behavioral equivalence we obtain,
in a systematic way, a coalgebraic underpinning of all quantitative
bisimulations discussed.Comment: In Proceedings QAPL 2015, arXiv:1509.0816
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
Reverse Bisimilarity vs. Forward Bisimilarity
Reversibility is the capability of a system of undoing its own actions starting from the last performed one, in such a way that a past consistent state is reached. This is not trivial for concurrent systems, as the last performed action may not be uniquely identifiable. There are several approaches to address causality-consistent reversibility, some including a notion of forward-reverse bisimilarity. We introduce a minimal process calculus for reversible systems to investigate compositionality properties and equational characterizations of forward-reverse bisimilarity as well as of its two components, i.e., forward bisimilarity and reverse bisimilarity, so as to highlight their differences. The study is conducted not only in a nondeterministic setting, but also in a stochastic one where time reversibility and lumpability for Markov chains are exploited
Syntactic Markovian Bisimulation for Chemical Reaction Networks
In chemical reaction networks (CRNs) with stochastic semantics based on
continuous-time Markov chains (CTMCs), the typically large populations of
species cause combinatorially large state spaces. This makes the analysis very
difficult in practice and represents the major bottleneck for the applicability
of minimization techniques based, for instance, on lumpability. In this paper
we present syntactic Markovian bisimulation (SMB), a notion of bisimulation
developed in the Larsen-Skou style of probabilistic bisimulation, defined over
the structure of a CRN rather than over its underlying CTMC. SMB identifies a
lumpable partition of the CTMC state space a priori, in the sense that it is an
equivalence relation over species implying that two CTMC states are lumpable
when they are invariant with respect to the total population of species within
the same equivalence class. We develop an efficient partition-refinement
algorithm which computes the largest SMB of a CRN in polynomial time in the
number of species and reactions. We also provide an algorithm for obtaining a
quotient network from an SMB that induces the lumped CTMC directly, thus
avoiding the generation of the state space of the original CRN altogether. In
practice, we show that SMB allows significant reductions in a number of models
from the literature. Finally, we study SMB with respect to the deterministic
semantics of CRNs based on ordinary differential equations (ODEs), where each
equation gives the time-course evolution of the concentration of a species. SMB
implies forward CRN bisimulation, a recently developed behavioral notion of
equivalence for the ODE semantics, in an analogous sense: it yields a smaller
ODE system that keeps track of the sums of the solutions for equivalent
species.Comment: Extended version (with proofs), of the corresponding paper published
at KimFest 2017 (http://kimfest.cs.aau.dk/
On the Expressiveness of Markovian Process Calculi with Durational and Durationless Actions
Several Markovian process calculi have been proposed in the literature, which
differ from each other for various aspects. With regard to the action
representation, we distinguish between integrated-time Markovian process
calculi, in which every action has an exponentially distributed duration
associated with it, and orthogonal-time Markovian process calculi, in which
action execution is separated from time passing. Similar to deterministically
timed process calculi, we show that these two options are not irreconcilable by
exhibiting three mappings from an integrated-time Markovian process calculus to
an orthogonal-time Markovian process calculus that preserve the behavioral
equivalence of process terms under different interpretations of action
execution: eagerness, laziness, and maximal progress. The mappings are limited
to classes of process terms of the integrated-time Markovian process calculus
with restrictions on parallel composition and do not involve the full
capability of the orthogonal-time Markovian process calculus of expressing
nondeterministic choices, thus elucidating the only two important differences
between the two calculi: their synchronization disciplines and their ways of
solving choices
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