Let E be a plane in an algebraic torus over an algebraically closed field. Given a balanced 1-dimensional fan C in the tropicalization of E, i. e. in the Bergman fan of the corresponding matroid, we give a complete algorithmic answer to the question whether or not C can be realized as the tropicalization of an algebraic curve contained in E. Moreover, in the case of realizability the algorithm ...

In [3], the following semantical picture of modified realizability is sketched: Consider the topos Set, whose objects are functions between sets, and whose arrows are commutative squares. The logic of Set corresponds to “Kripke forcing over a 2-element linear order”. Over Set, one can define the standard realizability topos Eff→ (not to be confused with Eff!). The modified realizability topos, ...

We are interested in implementing a fully automated software development process starting from sequence charts, which have proven their naturalness and usefulness in industry. We show in this paper that even for the simplest variants of sequence charts, there are strong impediments to the implementability of this dream. In the case of a manual development, we have to check the final implementat...

In [SR98] it has been shown that λ-calculus with control can be interpreted in any domain D which is isomorphic to the domain of functions from D to the 2-element (Sierpiński) lattice Σ. By a theorem of A. Pitts there exists a unique subset P of D such that f ∈ P iff f(~ d) = ⊥ for all ~ d ∈ P. The domain D gives rise to a realizability structure in the sense of [Kri11] where the set of proof-l...

We investigate automated reasoning techniques as a means of supporting authorization enforcement functions of security-aware workflow management systems. The aim of such support is that one may statically or dynamically guarantee the realizability of a workflow instance given the security constraints of the underlying workflow specification. We develop two such automated reasoning methods and e...

This paper considers compositional specifications of services using UML 2 collaborations, activity and interaction diagrams, and addresses the realizability problem for such specifications: given a global specification, can we construct a set of communicating system components whose joint behavior is precisely the specified global behavior? We approach the problem by looking at how the sequenci...