Two-sided strategy-proofness in many-to-many matching markets

We study the existence of group strategy-proof stable rules in many-to-many matching markets under responsiveness of agents’ preferences. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof mechanisms in many-to-many matching markets.

Rule 68: Contents of the Defence to the Statement for a declaration of non-infringement

Possible orders that can be applied for in the interim procedure are, in principle, all orders of the Court provided for in the UPCA and the Rules of Procedure. For a Statement of non-infringement, however, only a few orders may be relevant. Normally, the defendant in an action for a declaration of non-infringement does not lack any means of proof; therefore, all the rules on proof (Rule 190), on information (Rule 191), on preserving evidence (Rule 192), or on inspection (Rule 199) may be applicable in only a few cases. The reason for this is that the defendant has no direct advantage in the rejection of the claim (except for the cost decision in his favour). The defendant cannot enforce that decision, even if the Court decides positively on the infringement question. Claims arising out of an infringement are not the subject matter of the action. If the defendant wants to bring an infringement claim, he must do so in an infringement action (→ Art 33(6) UPCA).

A compiled implementation of normalisation by evaluation

We present a novel compiled approach to Normalisation by Evaluation (NBE) for ML-like languages. It supports efficient normalisation of open λ-terms with respect to β-reduction and rewrite rules. We have implemented NBE and show both a detailed formal model of our implementation and its verification in Isabelle. Finally we discuss how NBE is turned into a proof rule in Isabelle.

SEMI-AUTOMATIC DISTRIBUTED SYNTHESIS

We propose a sound and complete compositional proof rule for distributed synthesis. Applying our proof rule only requires the manual strengthening of the specification into a conjunction of formulas that can be guaranteed by individual black-box processes. All premises of the proof rule can be checked automatically. For this purpose, we give an automata-theoretic synthesis algorithm for single processes in distributed architectures. The behavior of the local environment of a process is unknown in the process of synthesis and cannot be assumed to be maximal. We therefore consider reactive environments that have the power to disable some of their own actions, and provide methods for synthesis (and realizability checking) in this setting. We establish upper bounds for CTL (2EXPTIME) and CTL* (3EXPTIME) synthesis with incomplete information, matching the known lower bounds for these problems, and provide matching upper and lower bounds for μ-calculus synthesis (2EXPTIME) with complete or incomplete information. Synthesis in reactive environments is harder than synthesis in maximal environments, where CTL, CTL* and μ-calculus synthesis are EXPTIME, 2EXPTIME and EXPTIME complete, respectively.