Web service choreographies specify conditions on observable interactions among the services. An important question in this regard is realizability: given a choreography C, does there exist a set of service implementations I that conform to C ? Further, if C is realizable, is there an algorithm to construct implementations in I ? We propose a local temporal logic in which choreographies can be s...

A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by V. Lifschitz in [15]. A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten [19]. In that paper he also extended Lifschitz’ realizability to second order arithmetic. The ...

This paper deals with the isotropic realizability of a given regular divergence free field j in R3 as a current field, namely to know when j can be written as σ∇u for some isotropic conductivity σ > 0, and some gradient field ∇u. The local isotropic realizability in R3 is obtained by Frobenius’ theorem provided that j and curl j are orthogonal in R3. A counter-example shows that Frobenius’ cond...

We present a general method for proving properties of typed λ-terms. This method is obtained by introducing a semantic notion of realizability which uses the notion of a cover algebra (as in abstract sheaf theory). For this, we introduce a new class of semantic structures equipped with preorders, called pre-applicative structures. These structures need not be extensional. In this framework, a g...

In this paper we study the realizability of a given smooth periodic gradient field ∇u defined in R, in the sense of finding when one can obtain a matrix conductivity σ such that σ∇u is a divergence free current field. The construction is shown to be always possible locally in R provided that ∇u is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fa...

We investigate the development of theories of types and computability via realizability. In the rst part of the thesis, we suggest a general notion of realizability, based on weakly closed partial cartesian categories, which generalizes the usual notion of realizability over a partial combinatory algebra. We show how to construct categories of so-called assemblies and modest sets over any weakl...

The relationship between three state space realizability conditions for nonlinear multi-input multi-output differential equations, formulated in terms of different mathematical tools, is studied. Moreover, explicit formulas are provided for calculation of the differentials of the state coordinates which, in case the necessary and sufficient realizability conditions are satisfied, can be integra...

In this paper, we define a new realizability semantics for the simply typed λμ-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability semantics using a particular term model. This paper corrects some errors in [21] by the first author and Saber.

In this paper, we define a realizability semantics for the simply typed λµ-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the computational behavior of some closed typed terms. We also prove a completeness result of our realizability semantics using a particular term model.

A celebrated theorem of Savitch [Sav70] states that NSPACE(S) ⊆ DSPACE(S). In particular, Savitch gave a deterministic algorithm to solve ST-CONNECTIVITY (an NL-complete problem) using O(logn) space, implying NL ⊆ DSPACE(logn). While Savitch’s theorem itself has not been improved in the last four decades, studying the space complexity of several special cases of STCONNECTIVITY has provided new ...