Unpacking Smart Contracts in the Legal Services: a systematic literature review

This paper employs a systematic literature review to construct a theoretical framework for the design of smart contracts in the field of legal services. The analysis of 32 studies is categorized into two types: descriptive and thematic. The descriptive analysis reveals that smart contracts serve as the foundation of current knowledge in this domain. Subsequently, a cyclical conceptual model is developed, illustrating the evolutionary progression of legal smart contracts and their interplay with preceding actions. Furthermore, the thematic analysis critically examines the literature, identifying challenges and concerns related to legal service offerings. The proposed model is then briefly applied to address these issues

Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime

The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are known to map (even high-order differentiable) polynomial-time computable functions to instances which are `hard' for classical complexity classes NP, #P, and CH; but, restricted to analytic functions, map polynomial-time computable ones to polynomial-time computable ones -- non-uniformly! We investigate the uniform parameterized complexity of the above operators in the setting of Weihrauch's TTE and its second-order extension due to Kawamura&Cook (2010). That is, we explore which (both continuous and discrete, first and second order) information and parameters on some given f is sufficient to obtain similar data on Max(f) and int(f); and within what running time, in terms of these parameters and the guaranteed output precision 2^(-n). It turns out that Gevrey's hierarchy of functions climbing from analytic to smooth corresponds to the computational complexity of maximization growing from polytime to NP-hard. Proof techniques involve mainly the Theory of (discrete) Computation, Hard Analysis, and Information-Based Complexity