490 research outputs found
Tropical Fourier-Motzkin elimination, with an application to real-time verification
We introduce a generalization of tropical polyhedra able to express both
strict and non-strict inequalities. Such inequalities are handled by means of a
semiring of germs (encoding infinitesimal perturbations). We develop a tropical
analogue of Fourier-Motzkin elimination from which we derive geometrical
properties of these polyhedra. In particular, we show that they coincide with
the tropically convex union of (non-necessarily closed) cells that are convex
both classically and tropically. We also prove that the redundant inequalities
produced when performing successive elimination steps can be dynamically
deleted by reduction to mean payoff game problems. As a complement, we provide
a coarser (polynomial time) deletion procedure which is enough to arrive at a
simply exponential bound for the total execution time. These algorithms are
illustrated by an application to real-time systems (reachability analysis of
timed automata).Comment: 29 pages, 8 figure
Reliable fault-tolerant model predictive control of drinking water transport networks
This paper proposes a reliable fault-tolerant model predictive control applied to drinking water transport networks. After a fault has occurred, the predictive controller should be redesigned to cope with the fault effect. Before starting to apply the fault-tolerant control strategy, it should be evaluated whether the predictive controller will be able to continue operating after the fault appearance. This is done by means of a structural analysis to determine loss of controllability after the fault complemented with feasibility analysis of the optimization problem related to the predictive controller design, so as to consider the fault effect in actuator constraints. Moreover, by evaluating the admissibility of the different actuator-fault configurations, critical actuators regarding fault tolerance can be identified considering structural, feasibility, performance and reliability analyses. On the other hand, the proposed approach allows a degradation analysis of the system to be performed. As a result of these analyses, the predictive controller design can be modified by adapting constraints such that the best achievable performance with some pre-established level of reliability will be achieved. The proposed approach is tested on the Barcelona drinking water transport network.Postprint (author's final draft
Parametric LTL on Markov Chains
This paper is concerned with the verification of finite Markov chains against
parametrized LTL (pLTL) formulas. In pLTL, the until-modality is equipped with
a bound that contains variables; e.g., asserts that
holds within time steps, where is a variable on natural
numbers. The central problem studied in this paper is to determine the set of
parameter valuations for which the probability to
satisfy pLTL-formula in a Markov chain meets a given threshold , where is a comparison on reals and a probability. As for pLTL
determining the emptiness of is undecidable, we consider
several logic fragments. We consider parametric reachability properties, a
sub-logic of pLTL restricted to next and , parametric B\"uchi
properties and finally, a maximal subclass of pLTL for which emptiness of is decidable.Comment: TCS Track B 201
Reaction Cycles in Membrane Systems and Molecular Dynamics
We are considering molecular dynamics and (sequential) membrane systems
from the viewpoint of Markov chain theory. The first step is to understand the structure of
the configuration space, with respect to communicating classes. Instead of a reachability
analysis by traditional methods, we use the explicit monoidal structure of this space with
respect to rule applications. This leads to the notion of precycle, which is an element of
the integer kernel of the stoichiometric matrix. The generators of the set of precycles
can be effectively computed by an incremental algorithm due to Contejean and Devie.
To arrive at a characterization of cycles, we introduce the notion of defect, which is a
set of geometric constraints on a configuration to allow a precycle to be enabled, that
is, be a cycle. An important open problem is the effcient calculation of the defects. We
also discuss aspects of asymptotic behavior and connectivity, as well as give a biological
example, showing the usefulness of the method for model checking
The Underlying Complexities Impacting Accelerator Decision MakingâA Combined Methodological Analysis
Business accelerators play a key role in the initial critical stages of assessment of commercial viability, offering mentorship provision of funding and protection of intellectual property for product development and refinement. However, little is known about the decision making criteria and detailed analysis of the underlying criteria and interdependencies between the key factors used by accelerator organisations to fund start-ups. This study focusses on the decision making criteria utilised by a leading ÂŁ21M accelerator programme, largely funded by the European Regional Development Fund for initial stage funding and intellectual property protection for product and innovation commercialisation. We incorporate a multi-methodological interpretive based approach based on Dayâs âReal-Win-Worthâ framework to develop the interrelationships and ranking between the factors. The results highlight the significance and weighting attached to the factors associated with the technical competency of the proposer and evidence of demand existing for the product. We propose a new framework that models the key factor interrelationships offering additional insight to accelerator based decision making
Stochastic Control via Entropy Compression
We consider an agent trying to bring a system to an acceptable state by
repeated probabilistic action. Several recent works on algorithmizations of the
Lovasz Local Lemma (LLL) can be seen as establishing sufficient conditions for
the agent to succeed. Here we study whether such stochastic control is also
possible in a noisy environment, where both the process of state-observation
and the process of state-evolution are subject to adversarial perturbation
(noise). The introduction of noise causes the tools developed for LLL
algorithmization to break down since the key LLL ingredient, the sparsity of
the causality (dependence) relationship, no longer holds. To overcome this
challenge we develop a new analysis where entropy plays a central role, both to
measure the rate at which progress towards an acceptable state is made and the
rate at which noise undoes this progress. The end result is a sufficient
condition that allows a smooth tradeoff between the intensity of the noise and
the amenability of the system, recovering an asymmetric LLL condition in the
noiseless case.Comment: 18 page
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