On the Complexity of Temporal-Logic Path Checking

Given a formula in a temporal logic such as LTL or MTL, a fundamental problem is the complexity of evaluating the formula on a given finite word. For LTL, the complexity of this task was recently shown to be in NC. In this paper, we present an NC algorithm for MTL, a quantitative (or metric) extension of LTL, and give an NCC algorithm for UTL, the unary fragment of LTL. At the time of writing, MTL is the most expressive logic with an NC path-checking algorithm, and UTL is the most expressive fragment of LTL with a more efficient path-checking algorithm than for full LTL (subject to standard complexity-theoretic assumptions). We then establish a connection between LTL path checking and planar circuits, which we exploit to show that any further progress in determining the precise complexity of LTL path checking would immediately entail more efficient evaluation algorithms than are known for a certain class of planar circuits. The connection further implies that the complexity of LTL path checking depends on the Boolean connectives allowed: adding Boolean exclusive or yields a temporal logic with P-complete path-checking problem

A Rewriting Based Model for Probabilistic Distributed Object Systems

Concurrent and distributed systems have traditionally been modelled using nondeterministic transitions over configurations. The nondeterminism provides an abstraction over scheduling, network delays, failures and randomization. However a probabilistic model can capture these sources of nondeterminism more precisely and enable statistical analysis, simulations and reasoning. We have developed a general semantic framework for probabilistic systems using probabilistic rewriting. Our framework also allows nondeterminism in the system. In this paper, we briefly describe the framework and its application to concurrent object based systems such as actors. We also identify a su#ciently expressive fragment of the general framework and describe its implementation. The concepts are illustrated by a simple client-server example

Time for Statistical Model Checking of Real-Time Systems

Abstract. We propose the first tool for solving complex (some unde-cidable) problems of timed systems by using Statistical Model Checking (SMC). The tool monitors several runs of the system, and then relies on statistical algorithms to get an estimate of the correctness of the entire design. Contrary to other existing toolsets, ours relies on i) a natural stochastic semantics for networks of timed systems, ii) an engine capable to solve problems that are beyond the scope of classical model checkers, and iii) a friendly user interface.

Complementary approaches to understanding the plant circadian clock

Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock

Learning and Designing Stochastic Processes from Logical Constraints

Continuous time Markov Chains (CTMCs) are a convenient mathematical model for a broad range of natural and computer systems. As a result, they have received considerable attention in the theoretical computer science community, with many important techniques such as model checking being now mainstream. However, most methodologies start with an assumption of complete specification of the CTMC, in terms of both initial conditions and parameters. While this may be plausible in some cases (e.g. small scale engineered systems) it is certainly not valid nor desirable in many cases (e.g. biological systems), and it does not lead to a constructive approach to rational design of systems based on specific requirements. Here we consider the problems of learning and designing CTMCs from observations/ requirements formulated in terms of satisfaction of temporal logic formulae. We recast the problem in terms of learning and maximising an unknown function (the likelihood of the parameters) which can be numerically estimated at any value of the parameter space (at a non-negligible computational cost). We adapt a recently proposed, provably convergent global optimisation algorithm developed in the machine learning community, and demonstrate its efficacy on a number of non-trivial test cases

Social networking, social media and complex emergencies: an annotated bibliography

Andrew Skuse and Tait Brimacomb

A tutorial on interactive Markov chains

Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies

Temporal Logic Based Monitoring of Assisted Ventilation in Intensive Care Patients

We introduce a novel approach to automatically detect ineffective breathing efforts in patients in intensive care subject to assisted ventilation. The method is based on synthesising from data temporal logic formulae which are able to discriminate between normal and ineffective breaths. The learning procedure consists in first constructing statistical models of normal and abnormal breath signals, and then in looking for an optimally discriminating formula. The space of formula structures, and the space of parameters of each formula, are searched with an evolutionary algorithm and with a Bayesian optimisation scheme, respectively. We present here our preliminary results and we discuss our future research directions.\&nbsp;</p