Savi Maharaj

A Modal Logic for Full LOTOS based on Symbolic Transition Systems

Symbolic transition systems separate data from process behaviour by allowing the data to be uninstantiated Designing a HML like modal logic for these transition systems is interesting because of the subtle interplay between the quanti ers for the data and the modal operators quanti ers on transitions This paper presents the syntax and semantics of such a logic and discusses the design issues involved in its construction The logic has been shown to be adequate with respect to strong early bisimulation over symbolic transition systems derived from Full LOTOS We de ne what is meant by adequacy and discuss how we can reason about it with the aid of a mechanised theorem prover

Controlling epidemic spread by social distancing: do it well or not at all.

BackgroundExisting epidemiological models have largely tended to neglect the impact of individual behaviour on the dynamics of diseases. However, awareness of the presence of illness can cause people to change their behaviour by, for example, staying at home and avoiding social contacts. Such changes can be used to control epidemics but they exact an economic cost. Our aim is to study the costs and benefits of using individual-based social distancing undertaken by healthy individuals as a form of control.MethodsOur model is a standard SIR model superimposed on a spatial network, without and with addition of small-world interactions. Disease spread is controlled by allowing susceptible individuals to temporarily reduce their social contacts in response to the presence of infection within their local neighbourhood. We ascribe an economic cost to the loss of social contacts, and weigh this against the economic benefit gained by reducing the impact of the epidemic. We study the sensitivity of the results to two key parameters, the individuals’ attitude to risk and the size of the awareness neighbourhood.ResultsDepending on the characteristics of the epidemic and on the relative economic importance of making contacts versus avoiding infection, the optimal control is one of two extremes: either to adopt a highly cautious control, thereby suppressing the epidemic quickly by drastically reducing contacts as soon as disease is detected; or else to forego control and allow the epidemic to run its course. The worst outcome arises when control is attempted, but not cautiously enough to cause the epidemic to be suppressed. The next main result comes from comparing the size of the neighbourhood of which individuals are aware to that of the neighbourhood within which transmission can occur. The control works best when these sizes match and is particularly ineffective when the awareness neighbourhood is smaller than the infection neighbourhood. The results are robust with respect to inclusion of long-range, small-world links which destroy the spatial structure, regardless of whether individuals can or cannot control them. However, addition of many non-local links eventually makes control ineffective.ConclusionsThese results have implications for the design of control strategies using social distancing: a control that is too weak or based upon inaccurate knowledge, may give a worse outcome than doing nothing.

Studying the ML module system in HOL

In an earlier project of VanInwegen and Gunter, the dynamic semantics of the Core of Standard ML (SML) was encoded in the HOL theorem-prover. We extend this by adding the dynamic Module system. We then develop a possible dynamic semantics for a Module system with higher order functors and projections and discuss how we use these to prove that evaluation in the proposed system is a conservative extension, in an appropiate sense, of evaluation in the SML Module system.

Studying the ML Module System in Hol

In an earlier project [5] the dynamic semantics of the Core of Standard ML (SML) was encoded in the HOL theorem-prover. We extend this by adding the dynamic Module system. We then develop a possible dynamic semantics for a Module system with higher-order functors and encode this as well. Next we relate these two semantics via embeddings and projections and discuss how we can use these to state and to prove that evaluation in the proposed system is a conservative extension, in an appropriate sense, of evaluation in the SML Module system.

An Adequate Logic for Full LOTOS

We present a novel result for a logic for symbolic transition systems based on LOTOS processes. The logic is adequate with respect to bisimulation defined on symbolic transition systems.

Omnibus verification policies: a flexible, configurable approach to assertion-based software verification

The three main assertion-based verification approaches are: design by contract (DBC), extended static checking (ESC) and verified design by contract (VDBC). Each approach offers a different balance between rigour and ease of use making them appropriate in different situations. Our goal is to explore the use of these approaches together in a flexible way, enabling an application to be broken down into sections with different reliability requirements and different verification approaches used in each section. We explain the benefits of using the approaches together, present a set of guidelines to avoid potential conflicts and give an overview of how the Omnibus IDE provides support for the full range of assertion-based verification approaches within a single tool.

DISTRIBUTED STOCHASTIC HYBRID SYSTEMS

Abstract We consider a theoretical, but very general mathematical model of control systems, namely stochastic hybrid systems. Then we study how to define concurrency for these systems.

Flexible and configurable verification policies with Omnibus

The three main assertion-based verification approaches are: run-time assertion checking (RAC), extended static checking (ESC) and full formal verification (FFV). Each approach offers a different balance between rigour and ease of use, making them appropriate in different situations. Our goal is to explore the use of these approaches together in a flexible way, enabling an application to be broken down into parts with different reliability requirements and different verification approaches used in each part. We explain the benefits of using the approaches together, present a set of guidelines to avoid potential conflicts and give an overview of how the Omnibus IDE provides support for the full range of assertion-based verification approaches within a single tool.

A bio-economic ‘war game’ model to simulate plant disease incursions and test response strategies at the landscape scale

Loss of area freedom from invasive alien species can have serious food security implications and place huge responsibility on incursion response managers. They make critical decisions despite profound uncertainty surrounding invasion ecology, surveillance and control technology effectiveness and human behaviour. We propose a spatially-explicit model that can aid response managers in devising and testing management strategies in a virtual world where the costs of failure are negligible. We apply the model in a group-based decision setting in which participants practise responding to fictional disease incursions in a pome fruit production area in Australia. Using the model, the response management group was able to develop mutually satisfactory rules of thumb for the use of quarantine and destruction zones and for when to withdraw resources from eradication efforts.

Encoding Z-style schemas in type theory

A distinctive feature of the Z specification language is its Schema Calculus which allows specifications to be packaged and put together to form new specifications. We investigate methods of transporting the Schema Calculus to the type theory UTT. We first attempt a direct encoding of schemas as Σ-types. This turns out to be unsatisfactory because encoding the operations of the Schema Calculus requires the ability to perform computations on the syntax of schemas, so we develop methods in which this syntax is also represented. These methods also depend upon Σ-types but use them in an unconventional fashion. We define a notion of implementation of a schema and use the LEGO proof-checker to prove some theorems about the interaction between implementations and our encodings of the operations of the Z Schema Calculus.