A Notion of Dynamic Interface for Depth-Bounded Object-Oriented Packages

Programmers using software components have to follow protocols that specify when it is legal to call particular methods with particular arguments. For example, one cannot use an iterator over a set once the set has been changed directly or through another iterator. We formalize the notion of dynamic package interfaces (DPI), which generalize state-machine interfaces for single objects, and give an algorithm to statically compute a sound abstraction of a DPI. States of a DPI represent (unbounded) sets of heap configurations and edges represent the effects of method calls on the heap. We introduce a novel heap abstract domain based on depth-bounded systems to deal with potentially unboundedly many objects and the references among them. We have implemented our algorithm and show that it is effective in computing representations of common patterns of package usage, such as relationships between viewer and label, container and iterator, and JDBC statements and cursors

Term Graph Representations for Cyclic Lambda-Terms

We study various representations for cyclic lambda-terms as higher-order or as first-order term graphs. We focus on the relation between `lambda-higher-order term graphs' (lambda-ho-term-graphs), which are first-order term graphs endowed with a well-behaved scope function, and their representations as `lambda-term-graphs', which are plain first-order term graphs with scope-delimiter vertices that meet certain scoping requirements. Specifically we tackle the question: Which class of first-order term graphs admits a faithful embedding of lambda-ho-term-graphs in the sense that: (i) the homomorphism-based sharing-order on lambda-ho-term-graphs is preserved and reflected, and (ii) the image of the embedding corresponds closely to a natural class (of lambda-term-graphs) that is closed under homomorphism? We systematically examine whether a number of classes of lambda-term-graphs have this property, and we find a particular class of lambda-term-graphs that satisfies this criterion. Term graphs of this class are built from application, abstraction, variable, and scope-delimiter vertices, and have the characteristic feature that the latter two kinds of vertices have back-links to the corresponding abstraction. This result puts a handle on the concept of subterm sharing for higher-order term graphs, both theoretically and algorithmically: We obtain an easily implementable method for obtaining the maximally shared form of lambda-ho-term-graphs. Also, we open up the possibility to pull back properties from first-order term graphs to lambda-ho-term-graphs. In fact we prove this for the property of the sharing-order successors of a given term graph to be a complete lattice with respect to the sharing order. This report extends the paper with the same title (http://arxiv.org/abs/1302.6338v1) in the proceedings of the workshop TERMGRAPH 2013.Comment: 35 pages. report extending proceedings article on arXiv:1302.6338 (changes with respect to version v2: added section 8, modified Proposition 2.4, added Remark 2.5, added Corollary 7.11, modified figures in the conclusion

Threshold graph limits and random threshold graphs

We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.Comment: 47 pages, 8 figure