We study the notion of safe realizability for high-level message sequence charts (HMSCs) (Proceedings of the 28th International Colloquium on Automata, Languages and Programming (ICALP 2001), Crete (Greece), Lecture Notes in Computer Science, Vol. 2076, Springer, Berlin, 2001, pp. 797–808). We show that safe realizability is EXPSPACE-complete for bounded HMSCs but undecidable for the class of a...

We show that every geometric morphism between realizability toposes satisfies the condition that its inverse image commutes with the ‘constant object’ functors, which was assumed by John Longley in his pioneering study of such morphisms. We also provide the answer to something which was stated as an open problem on Jaap van Oosten’s book on realizability toposes: if a subtopos of a realizabilit...

In this dissertation we collect some results about “interactive realizability”, a realizability semantics that extends the Brouwer-Heyting-Kolmogorov interpretation to (sub-)classical logic, more precisely to first-order intuitionistic arithmetic (Heyting Arithmetic, HA) extended by the law of the excluded middle restricted to Σ1 formulas (EM1), a system motivated by its interest in proof minin...

We study a notion of realizability with a local operator J which was first considered by A.M. Pitts in his thesis [7]. Using the Suslin-Kleene theorem, we show that the representable functions for this realizability are exactly the hyperarithmetical (∆11) functions. We show that there is a realizability interpretation of nonstandard arithmetic, which, despite its classical character, lives in a...

Linear Temporal Logic (LTL) is the de-facto standard temporal logic for system specification, whose foundational properties have been studied over five decades. Safety and cosafety of LTL define notable fragments LTL, where a prefix trace suffices to establish whether formula true or not that trace. In this paper, we study complexity problems satisfiability, validity, realizability infinite fin...