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The promising markets for voluntary carbon credits are faced with crippling challenges to the certification of carbon sequestration and the lack of scalable market infrastructure in which companies and institutions can invest in carbon offsetting. This amounts to a funding problem for green transition projects, such as in the agricultural sector, since farmers need access to the liquidity needed to fund the transition to sustainable practices. We explore the feasibility of mitigating infrastructural challenges based on a DLT Trading and Settlement System for green bonds. The artefact employs a multi-sharded architecture in which the nodes retain carefully orchestrated responsibilities in the functioning of the network. We evaluate the artefact in a supranational context with an EU-based regulator as part of a regulatory sandbox program targeting the new EU DLT Pilot regime. By conducting design-driven research with stakeholders from industrial and governmental bodies, we contribute to the IS literature on the practical implications of DLT.

We characterize digital cash as the digital equivalent of physical cash: secure, fungible, decentralized, directly controlled, privacy-preserving; but enhanced with qualitatively new functionality. It is extremely efficiently transferable and, most importantly, transactional or, more generally, contract-backed. This facilitates fully automated, guaranteed transactional execution of atomic resource exchanges and more complex contracts, without a multitude of intermediaries and expensive or slow semi-manual processes. A didactic objective is separating money characteristics from technology aspects such as specific blockchain and distributed ledger systems to help disentangle discussions of digital money design from implementation techniques. We finally discuss the power and role of programmable (contract-backed) digital money in case studies: tokenization of invoice debt using smart contracts on Ethereum, with stablecoins serving as digital money; smart contracts for disbursing payments transparently and reliably in accordance with social legislation; and a Danish e-krone for crowdfunding public and private community projets. These contributions are made in independent chapters by participants of the Working Group on Digital Cash at Copenhagen FinTech in 2018 and 2019, which have not been published before. Collectively, the contributions illustrate the design space and potential of digital money when powered by smart digital contracts that effectively eliminate both counterparty risk (somebody does not pay or does not deliver) and settlement risk (a trade fails and needs to be aborted) orders of magnitude faster than in current financial practice., Comment: Editor: Fritz Henglein. Authors: Fritz Henglein (Chapters 1, 2, 3, 5), Fritz Henglein and Christian Olesen (Chapter 4), Gert Sylvest (Chapter 6), S{\o}ren Debois (Chapter 7), Morten C. Nielsen and Christian Olesen (Chapter 8)

We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we obtain compact and computationally efficient data structures for data collections corresponding to union and deletion, repeated union, Cartesian product and key-indexed data. Free modules naturally give rise to polysets, which generalise multisets and facilitate expressing database queries as multilinear maps with asymptotically efficient evaluation on polyset constructors. We introduce compact maps as a way of representing infinite (poly)sets constructible from an infinite base set and its elements by addition and subtraction. We show how natural joins generalise to algebraic joins, while intersection is implemented by a novel algorithm on nested compact maps that carefully avoids visiting parts of the input that do not contribute to the eventual output. Our algebraic framework leads to a worst-case optimal evaluation of cyclic relational queries, which is known to be impossible using textbook query optimisers that operate on lists of records only., Comment: In Proceedings MSFP 2022, arXiv:2206.09534

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars, vectors, matrices or tensors represented as multi-dimensional arrays. We show that both symbolic and automatic differentiation can be performed using a differential calculus for generating linear functions representing Fr\'echet derivatives based on rules for primitive, constant, linear and bilinear functions as well as their sequential and parallel composition. Linear functions are represented in a combinatory domain-specific language. Finally, we provide a calculus for symbolically computing the adjoint of a derivative without using matrices, which are too inefficient to use on high-dimensional spaces. The resulting symbolic representation of a derivative retains the data-parallel operations from the input program. The combination of combinatory differentiation and computing formal adjoints turns out to be behaviorally equivalent to reverse-mode automatic differentiation. In particular, it provides opportunities for optimizations where matrices are too inefficient to represent linear functions., Comment: In Proceedings MSFP 2022, arXiv:2206.09534

Sharding is the prevalent approach to breaking the trilemma of simultaneously achieving decentralization, security, and scalability in traditional blockchain systems, which are implemented as replicated state machines relying on atomic broadcast for consensus on an immutable chain of valid transactions. Sharding is to be understood broadly as techniques for dynamically partitioning nodes in a blockchain system into subsets (shards) that perform storage, communication, and computation tasks without fine-grained synchronization with each other. Despite much recent research on sharding blockchains, much remains to be explored in the design space of these systems. Towards that aim, we conduct a systematic analysis of existing sharding blockchain systems and derive a conceptual decomposition of their architecture into functional components and the underlying assumptions about system models and attackers they are built on. The functional components identified are node selection, epoch randomness, node assignment, intra-shard consensus, cross-shard transaction processing, shard reconfiguration, and motivation mechanism. We describe interfaces, functionality, and properties of each component and show how they compose into a sharding blockchain system. For each component, we systematically review existing approaches, identify potential and open problems, and propose future research directions. We focus on potential security attacks and performance problems, including system throughput and latency concerns such as confirmation delays. We believe our modular architectural decomposition and in-depth analysis of each component, based on a comprehensive literature study, provides a systematic basis for conceptualizing state-of-the-art sharding blockchain systems, proving or improving security and performance properties of components, and developing new sharding blockchain system designs.

We give a natural complete infinitary axiomatization of the equational theory of the context-free languages, answering a question of Lei{\ss} (1992)., Comment: In Proceedings FICS 2013, arXiv:1308.5896