Realizability – checking whether a specification can be implemented by an open system – is a fundamental step in the design flow. However, if the specification turns out not to be realizable, there is no method to pinpoint the causes for unrealizability. In this paper, we address the open problem of providing diagnostic information for realizability: we formally define the notion of (minimal) e...

In this paper we use the concept of integer-pair sequences, an invariant of graphs and digraphs introduced in Hakimi and Patrinos [9], and results on its unique realizability, in Das [4,5], to obtain results on the unique realizability of degree sequences, another invariant of graphs and digraphs. We thus present a unified approach to solving the problem of unique realizability of these two inv...

We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of pole and proof-like term. This method does in particular allow to associate realizability models to computable functions. Following recent work of Streicher ...

Specification, modeling and analysis of interactions among peers that communicate via messages are becoming increasingly important due to the emerging area of web services. Collaboration diagrams provide a convenient visual model for characterizing such interactions. An interaction can be characterized as a global sequence of messages exchanged among a set of peers, listed in the order they are...

This paper introduces an optimization strategy for evaluating the realizability of a 2D wireframe sketch that conveys geometric and topological information about a 3D solid model. Applying the cross-section realizability criterion, one is able to assert whether a wireframe sketch is a true orthogonal projection of a 3D-solid. In this work, we first review current sketch interpretation methods a...

In [6, 7, 9], we have introduced the technique of classical realizability, which permits to extend the Curry-Howard correspondence between proofs and programs [5], to ZermeloFraenkel set theory. The models of ZF we obtain in this way are called realizability models ; this technique is an extension of the method of forcing, in which the ordered sets (sets of conditions) are replaced with more co...

We introduce a category of basic combinatorial objects, encompassing PCAs and locales. Such a basic combinatorial object is to be thought of as a pre-realizability notion. To each such object we can associate an indexed preorder, generalizing the construction of triposes for various notions of realizability. There are two main results: first, the characterization of triposes which arise in this...