In this short note, we consider the optimization variant of the realizability problem for specifications in Prompt Linear Temporal Logic (Prompt-LTL), which extends Linear Temporal Logic (LTL) by the prompt eventually operator whose scope is bounded by a parametric bound. In the realizability optimization problem, one is interested in computing the optimal bound that allows to realize a given s...

Over the last few years, the automata-theoretic approach to realizability checking and synthesis of reactive modules, developed by Pnueli and Rosner, by Abadi, Lamport, and Wolper, and by Dill and Wong-Toi, has been quite successful, handling both the synchronous and the asynchronous cases. In this approach one transforms the specification into a tree automaton. The specification is realizable ...

Kobayashi, S. and M. Tatsuta, Realizability interpretation of generalized inductive definitions, Theoretical Computer Science 131 (1994) 121-138. Generalized inductive definitions give a way of defining a predicate as the least solution P of the equation P-A [P] where a predicate variable P may occur in a formula A[P] positively. This paper gives a q-realizability interpretation of generalized ...

SYSTEMS Yuan Wang Mathematics Department, Florida Atlantic University, Boca Raton, Fl 33431 (407)367-3317, E-mail: y [email protected] Eduardo D. Sontag Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 (908)932-3072, E-mail: [email protected] ABSTRACT An equivalence is shown between realizability of input/output operators by rational control systems and high orde...

We define a notion of relational linear combinatory algebra (rLCA) which is a generalization of a linear combinatory algebra defined by Abramsky, Haghverdi and Scott. We also define a category of assemblies as well as a category of modest sets which are realized by rLCA. This is a linear style of realizability in a way that duplicating and discarding of realizers is allowed in a controlled way....

Contextual bandit learning is a reinforcement learning problem where the learner repeatedly receives a set of features (context), takes an action and receives a reward based on the action and context. We consider this problem under a realizability assumption: there exists a function in a (known) function class, always capable of predicting the expected reward, given the action and context. Unde...

A conversation protocol specifies the desired global behaviors of a web service composition in a top-down fashion. Before implementing a conversation protocol, its realizability has to be determined, i.e., can a bottom-up web service composition be synthesized so that it generates exactly the same set of conversations as specified by the protocol? This chapter presents three sufficient conditio...

A unified view over well-known interpretations of intuitionistic logic, such as Gödel’s dialectica interpretation [6], Diller-Nahm interpretation [1] and Kreisel’s modified realizability [7] was achieved through a parametrised interpretation in the intuitionistic logic context [8] but also, very elegantly, in the linear logic setting (see [10], [9] and [3]). In this talk we report on work in pr...

In the €rst parts of this thesis, we introduced several calculi for which we gave a Krivine realizability interpretation. Namely, in addition to Krivine’s λc -calculus, we presented interpretations for the callby-name, call-by-value and call-by-need λμμ̃-calculi, for dLt̂p and for dLPAω . Amongst others, we could cite Munch-Maccagnoni’s interpretation for System L [126], Lepigre’s interpretation ...

Realizability for knowledge representation formalisms studies the following question: Given a semantics and a set of interpretations, is there a knowledge base whose semantics coincides exactly with the given interpretation set? We introduce a general framework for analyzing realizability in abstract dialectical frameworks (ADFs) and various of its subclasses. In particular, the framework appli...