Consensus halving is PPA-complete

We show that the computational problem Consensus Halving is PPA-Complete, the first PPA-Completeness result for a problem whose definition does not involve an explicit circuit. We also show that an approximate version of this problem is polynomial-time equivalent to Necklace Splitting, which establishes PPAD-hardness for Necklace Splitting and suggests that it is also PPA-Complete

Certified Symbolic Management of Financial Multi-party Contracts

Domain-specific languages (DSLs) for complex financial contracts are in practical use in many banks and financial institutions to-day. Given the level of automation and pervasiveness of software in the sector, the financial domain is immensely sensitive to soft-ware bugs. At the same time, there is an increasing need to analyse (and report on) the interaction between multiple parties. In this pa-per, we present a multi-party contract language that rigorously rel-egates any artefacts of simulation and computation from its core, which leads to favourable algebraic properties, and therefore al-lows for formalising domain-specific analyses and transformations using a proof assistant. At the centre of our formalisation is a sim-ple denotational semantics independent of any stochastic aspects. Based on this semantics, we devise certified contract analyses and transformations. In particular, we give a type system, with an ac

The complexity of splitting necklaces and bisecting ham sandwiches

We resolve the computational complexity of two problems known as Necklace Splitting and Discrete Ham Sandwich, showing that they are PPA-complete. For Necklace Splitting, this result is specific to the important special case in which two thieves share the necklace. We do this via a PPA-completeness result for an approximate version of the Consensus Halving problem, strengthening our recent result that the problem is PPA-complete for inverse-exponential precision. At the heart of our construction is a smooth embedding of the high-dimensional Mobius strip in the Consensus Halving problem. These results settle the status of PPA as a class that captures the complexity of “natural” problems whose definitions do not incorporate a circuit