<p>Quite often modelers with constraint programming (CP) use the same modelling patterns for different problems, possibly from different domains. This results in recurring idioms in constraint programs. Our approach can be seen as a three-step approach. First, we identify some of these recurring patterns in constraint programs. Second, we propose a general way of describing these patterns by introducing proper constructs that would cover a wide range of applications. Third, we propose automating the process of reproducing these idioms from these higher-level descriptions. The whole process can be seen as a way of encapsulating some of the expertise and knowledge often used by CP modelers and making it available in much simpler forms. Doing so, we are able to extend current CP languages with high-level abstractions that open doors for automation of some of the modelling processes.</p><p>In particular, we introduce function variables and allow the statement of constraints on these variables using function operations. A <i>function variable</i> is a decision variable that can take a value from a set of functions as opposed to an <i>integer variable</i> that ranges over integers, or a <i>set variable</i> that ranges over a set of sets. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a function model expressed using function variables opens doors to the automatic generation of alternate CP models. These alternate models either use a different variable representation, or have extra implied constraints, or employ different constraint formulation, or combine different models that are linked using channelling constraints. A number of heuristics are also developed that allow the comparison of different constraint formulations. Furthermore, we present an extensive theoretical comparison of models of injection problems supported by asymptotic and empirical studies. Finally, a practical modelling tool that is built based on a high-level language that allows function variables is presented and evaluated. The tool helps users explore different alternate CP models starting from a function model that is easier to develop, understand, and maintain.</p>

Quite often modelers with constraint programming (CP) use the same modelling patterns for different problems, possibly from different domains. This results in recurring idioms in constraint programs. Our approach can be seen as a three-step approach. First, we identify some of these recurring patterns in constraint programs. Second, we propose a general way of describing these patterns by introducing proper constructs that would cover a wide range of applications. Third, we propose automating the process of reproducing these idioms from these higher-level descriptions. The whole process can be seen as a way of encapsulating some of the expertise and knowledge often used by CP modelers and making it available in much simpler forms. Doing so, we are able to extend current CP languages with high-level abstractions that open doors for automation of some of the modelling processes. In particular, we introduce function variables and allow the statement of constraints on these variables using function operations. A function variable is a decision variable that can take a value from a set of functions as opposed to an integer variable that ranges over integers, or a set variable that ranges over a set of sets. We show that a function variable can be mapped into different representations in terms of integer and set variables, and illustrate how to map constraints stated on a function variable into constraints on integer and set variables. As a result, a function model expressed using function variables opens doors to the automatic generation of alternate CP models. These alternate models either use a different variable representation, or have extra implied constraints, or employ different constraint formulation, or combine different models that are linked using channelling constraints. A number of heuristics are also developed that allow the comparison of different constraint formulations. Furthermore, we present an extensive theoretical comparison of models of injection problems supported by asymptotic and empirical studies. Finally, a practical modelling tool that is built based on a high-level language that allows function variables is presented and evaluated. The tool helps users explore different alternate CP models starting from a function model that is easier to develop, understand, and maintain.

<p>Many computer systems in our daily life require highly available applications (such as medical equipment) and some others run on difficult to access places (such as satellites). These systems are subject to a variety of potential failures that may degrade their performance. Therefore, being able to reason about faults and their impact on systems is gaining considerable attention. Existing work on fault tolerance is mostly focused on addressing faults at the programming language level. In the recent past, significant efforts have been made to use formal methods to specify and verify fault tolerant systems to provide more reliable software. Related with this, some researchers have pointed out that Deontic Logic is useful for reasoning about fault tolerant systems due to its expressive nature in relation to defining norms, used to describe expected behaviour and prescribing what happens when these norms are violated.</p> <p>In this thesis, we demonstrate how Deontic Logic can be used to model an existing real world problem concerning fault tolerance mechanisms. We consider different situations that a vehicle faces on the road and the consequent reactions of the driver or vehicle based on good and bad behaviour. We got the idea and motivation for this case study from the SASPENCE sub-project, conducted under the European Integrated Project PReVENT. This sub-project focuses on a vehicle’s behaviour in maintaining safe speed and safe distance on the road. As our first modelling attempt, we use a Propositional Deontic Logic approach, to justify to what extent we can apply this Logical approach to model a real world problem. Subsequently, we use a First Order Deontic Logic approach, as it can incorporate the use of parameters and quantification over them, which is more useful to model real world scenarios.</p> <p>We state and prove some interesting expected properties of the models using a First Order proof system. Based on these modelling exercises, we acquired different engineering ideas and lessons, and present them in this thesis in order to aid modelling of future fault tolerant systems.</p> / Master of Science (MSc)