11,440 research outputs found
Abstract Interpretation for Probabilistic Termination of Biological Systems
In a previous paper the authors applied the Abstract Interpretation approach
for approximating the probabilistic semantics of biological systems, modeled
specifically using the Chemical Ground Form calculus. The methodology is based
on the idea of representing a set of experiments, which differ only for the
initial concentrations, by abstracting the multiplicity of reagents present in
a solution, using intervals. In this paper, we refine the approach in order to
address probabilistic termination properties. More in details, we introduce a
refinement of the abstract LTS semantics and we abstract the probabilistic
semantics using a variant of Interval Markov Chains. The abstract probabilistic
model safely approximates a set of concrete experiments and reports
conservative lower and upper bounds for probabilistic termination
An Analysis for Proving Probabilistic Termination of Biological Systems
In this paper we apply the abstract interpretation approach
for approximating the behavior of biological systems, modeled specifically using the
Chemical Ground Form calculus, a simple stochastic calculus rich enough to model the dynamics of biochemical reactions.
The analysis is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting
the multiplicity of reagents present in a solution,
using intervals. For abstracting the probabilistic semantics, modeled as a
Discrete-Time Markov Chain, we use a variant of Interval Markov Chains, where probabilistic and non-deterministic
steps are combined together. The abstract probabilistic semantics
is systematically derived from an abstract Labeled Transition System.
The abstract probabilistic model
safely approximates the set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination
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A Monte Carlo model checker for probabilistic LTL with numerical constraints
We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc).
We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation
using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking
of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or
stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach
allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints
over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes
one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of
variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on
intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical
systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach
for the structured formal engineering of biological systems
GSOS for non-deterministic processes with quantitative aspects
Recently, some general frameworks have been proposed as unifying theories for
processes combining non-determinism with quantitative aspects (such as
probabilistic or stochastically timed executions), aiming to provide general
results and tools. This paper provides two contributions in this respect.
First, we present a general GSOS specification format (and a corresponding
notion of bisimulation) for non-deterministic processes with quantitative
aspects. These specifications define labelled transition systems according to
the ULTraS model, an extension of the usual LTSs where the transition relation
associates any source state and transition label with state reachability weight
functions (like, e.g., probability distributions). This format, hence called
Weight Function SOS (WFSOS), covers many known systems and their bisimulations
(e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS,
Segala-GSOS, among others).
The second contribution is a characterization of these systems as coalgebras
of a class of functors, parametric on the weight structure. This result allows
us to prove soundness of the WFSOS specification format, and that
bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Model checking probabilistic and stochastic extensions of the pi-calculus
We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature
A Taxonomy of Causality-Based Biological Properties
We formally characterize a set of causality-based properties of metabolic
networks. This set of properties aims at making precise several notions on the
production of metabolites, which are familiar in the biologists' terminology.
From a theoretical point of view, biochemical reactions are abstractly
represented as causal implications and the produced metabolites as causal
consequences of the implication representing the corresponding reaction. The
fact that a reactant is produced is represented by means of the chain of
reactions that have made it exist. Such representation abstracts away from
quantities, stoichiometric and thermodynamic parameters and constitutes the
basis for the characterization of our properties. Moreover, we propose an
effective method for verifying our properties based on an abstract model of
system dynamics. This consists of a new abstract semantics for the system seen
as a concurrent network and expressed using the Chemical Ground Form calculus.
We illustrate an application of this framework to a portion of a real
metabolic pathway
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