Inferring Argument Size Relationships with CLP(R)

Argument size relationships are useful in termination analysis which, in turn, is important in program synthesis and goal-replacement transformations. We show how a precise analysis for inter-argument size relationships, formulated in terms of abstract interpretation, can be implemented straightforwardly in a language with constraint support like CLP(R) or SICStus version 3. The analysis is based on polyhedral approximations and uses a simple relaxation technique to calculate least upper bounds and a delay method to improve the precision of widening. To the best of our knowledge, and despite its simplicity, the analysis derives relationships to an accuracy that is either comparable or better than any existing technique

Evaluating the Comprehension of Euler Diagrams

We describe an empirical investigation into layout criteria that can help with the comprehension of Euler diagrams. Euler diagrams are used to represent set inclusion in applications such as teaching set theory, database querying, software engineering, filing system organisation and bio-informatics. Research in automatically laying out Euler diagrams for use with these applications is at an early stage, and our work attempts to aid this research by informing layout designers about the importance of various Euler diagram aesthetic criteria. The three criteria under investigation were: contour jaggedness, zone area inequality and edge closeness. Subjects were asked to interpret diagrams with different combinations of levels for each of the criteria. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of their importance

Lower-bound Time-Complexity Analysis of Logic Programs

The paper proposes a technique for inferring conditions on goals that, when satisfied, ensure that a goal is sufficiently coarse-grained to warrant parallel evaluation. The method is powerful enough to reason about divide-and-conquer programs, and in the case of quicksort, for instance, can infer that a quicksort goal has a time complexity that exceeds 64 resolution steps (a threshold for spawning) if the input list is of length 10 or more. This gives a simple run-time tactic for controlling spawning. The method has been proved correct, can be implemented straightforwardly, has been demonstrated to be useful on a parallel machine, and, in contrast with much of the previous work on time-complexity analysis of logic programs, does not require any complicated difference equation solving machinery

A Study into the Comprehension of Euler Diagrams

We describe an empirical investigation into some of the layout criteria that may facilitate the comprehension of Euler diagrams. The three criteria under investigation were: smoothness, zone area equality and edge closeness. Subjects were asked to interpret diagrams that had good and bad levels of each criterion. The goal of this research is an initial step into using empirical evidence to support decisions concerning the metrics used for automated layout of Euler diagrams. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of importance for these criteria

An Isomorphism between Abstract Polyhedral Cones and Definite Boolean Functions

Polyhedral cones can be represented by sets of linear inequalities that express inter-variable relationships. These inequalities express inter-variable relationships that are quantified by the ratios between the variable coefficients. However, linear inequalities over a non-negative variable domain with only unit variable coefficients and no constants other than zero can represent relationships that can be valid in non-numeric domains. For instance, if variables are either non-negative or zero itself, that is, a strictly two-point domain, then 0 <= x, 0 <= y, x <= y, expresses a dependency between x and y, since if y is known to be zero, then so is x. By defining an abstraction operator that effectively puts aside the scaling coefficients whilst retaining the inter-variable aspect of these relationships polyhedral cones can express the same dependency information as Def, a class of Boolean function. Boolean functions are considered over a fixed finite set of variables and Def is a subset of the positive Boolean functions, which return the value true when every variable returns true. Def is a complete lattice ordered by logical consequence and it will be shown that the abstract cones also form a complete lattice, ordered by set inclusion, that is isomorphic to Def

Evaluating the Comprehension of Euler Diagrams

We describe an empirical investigation into layout criteria that can help with the comprehension of Euler diagrams. Our work is intended to inform automatic Euler diagram layout research by confirming the importance of various Euler diagram aesthetic criteria. The three criteria under investigation were: smoothness, zone area equality and edge closeness. Subjects were asked to interpret diagrams with different combinations of levels for each of the criteria. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of importance for the criteria

Using Games to Investigate Movement for Graph Comprehension

We describe the results of empirical investigations that explore the effectiveness of moving graph diagrams to improve the comprehension of their structure. The investigations involved subjects playing a game that required understanding the structure of a number of graphs. The use of a game as the task was intended to motivate the exploration of the graph by the subjects. The results show that movement can be beneficial when there is node-node or node-edge occlusion in the graph diagram but can have a detrimental effect when there is no occlusion, particularly if the diagram is small. We believe the positive result should generalise to other graph exploration tasks, and that graph movement is likely be useful as an additional graph exploration tool

Computing Convex Hulls with a Linear Solver

A programming tactic involving polyhedra is reported that has been widely applied in the polyhedral analysis of (constraint) logic programs. The method enables the computations of convex hulls that are required for polyhedral analysis to be coded with linear constraint solving machinery that is available in many Prolog systems