Abstract. Today, two distinct direct approaches to prove termination of CHR programs exist. The first approach, by T. Frühwirth, proves termination of CHR programs without propagation. The second, by Voets et al., deals with programs that contain propagation. It is however less powerful on programs without propagation. In this paper, we present new termination conditions that are strictly more powerful than those from previous approaches and that are also applicable to a new class of programs. Furthermore, we present a new representation for CHR states for which size-decreases between consecutive states correspond to termination. Both contributions are linked: our termination conditions correspond to the existence of a well-founded order on the new state representation, which decreases for consecutive computation states.

No abstract

We propose a new constraint-based approach to termination analysis, applicable to Logic Programming (LP) and Constraint Handling Rules (CHR). Our approach further extends the existing constraintbased approaches for LP based on polynomial interpretations and introduces a whole new level of expressivity. We can handle problems such as bounded increase and integer arithmetic, elegantly. Furthermore, we are able to prove termination of programs that only terminate for subsets of the considered queries. Examples are algorithms that manipulate graphs and that only terminate if the graph in the input is cycle-free. This information cannot be represented, using the existing techniques in termination analysis. Therefore, we introduce invariance relations, representing relations among terms that hold on atoms during calls to the program. These relations can also be derived in a constraint-based manner and they can be used as a basis for a more expressive interpretation of the atoms of the program. We discuss our technique in the context of CHR, solving an important class of open problems containing transitivity rules. We also demonstrate the technique in an LP context and show that it is more powerful than existing constraint-based approaches. The following CHR program [3, 7], computes the transitive closure of a graph. transitivity @ arc(X, Y), arc(Y, Z) ⇒ arc(X, Z).

In the past few years, several successful approaches to termination analysis of Constraint Handling Rules (CHR) have been proposed. In parallel to these developments, for termination analysis of Logic Programs (LP), recent work has shown that a stronger focus on the analysis of the cycles in the strongly connected components (SCC) of the program is very beneficial, both for precision and efficiency of the analysis. In this paper we investigate the benefit of using the cycles of the SCCs of CHR programs for termination analysis. It is a non-trivial task to define the notion of a cycle for a CHR program. We introduce the notion of a self-sustaining set of CHR rules and show that it provides a natural counterpart for the notion of a cycle in LP. We prove that non-selfsustainability of an SCC in a CHR program entails termination for all queries to that SCC. Then, we provide an efficient way to prove that an SCC of a CHR program is non-self-sustainable, providing an additional, new way of proving termination of (part of) the program. We integrate these ideas into the CHR termination analyser CHRisTA and demonstrate by means of experiments that this extension significantly improves both the efficiency and the performance of the analyser.

Automated surface vessels must integrate many tasks and motions at the same time. Moreover, vessels as well as monitoring and control services need to react to physical disturbances, to dynamically allocate software resources available within a particular environment, and to communicate with various other actors in particular navigation and traffic situations. In this work, the responsibility for the situational awareness is given to a mediator that decides how: 1) to assess the impact of the actual physical environment on the quality and performance of the ongoing task executions; 2) to make sure these tasks satisfy the system requirements; and 3) to be robust against disturbances. This paper proposes a set of semantic world models within the context of inland waterway transport, and discusses policies and methodologies to compose, use, and connect these models. Model-conform entities and relations are composed dynamically, that is, corresponding to the opportunities and challenges offered by the actual situation. The semantic world models discussed in this work are divided into two main categories: 1) the semantic description of a vessel’s own properties and relationships, called the internal world model, or body model, and 2) the semantic description of its local environment, called the external world model, or map. A range of experiments illustrate the potential of using such models to decide the reactions of the application at runtime. Furthermore, three dynamic, context-dependent, ship domains are integrated in the map as two-dimensional geometric entities around a moving vessel to increase the situational awareness of automated vessels. Their geometric representations depend on the associated relations; for example, with: 1) the motion of the vessel, 2) the actual, desired, or hypothesised tasks, 3) perception sensor information, and 4) other geometries, e.g., features from the Inland Electronic Navigational Charts. The ability to unambiguously understand the environmental context, as well as the motion or position of surrounding entities, allows for resource-efficient and straightforward control decisions. The semantic world models facilitate knowledge sharing between actors, and significantly enhance explainability of the actors’ behaviour and control decisions.