Related papers: An Invariant Cost Model for the Lambda Calculus
The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to…
Performing $n$ steps of $\beta$-reduction to a given term in the $\lambda$-calculus can lead to an increase in the size of the resulting term that is exponential in $n$. The same is true for the possible depth increase of terms along a…
Adaptive inference schemes reduce the cost of machine learning inference by assigning smaller models to easier examples, attempting to avoid invocation of larger models when possible. In this work we explore a simple, effective adaptive…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
Natural learners must compute an estimate of future outcomes that follow from a stimulus in continuous time. Widely used reinforcement learning algorithms discretize continuous time and estimate either transition functions from one step to…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
We consider computations of a Turing machine subjected to noise. In every step, the action (the new state and the new content of the observed cell, the direction of the head movement) can differ from that prescribed by the transition…
We present a formulation of the transaction cost analysis (TCA) in the Bayesian framework for the primary purpose of comparing broker algorithms using standardized benchmarks. Our formulation allows effective calculation of the expected…
The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
We consider dynamic pricing with covariates under a generalized linear demand model: a seller can dynamically adjust the price of a product over a horizon of $T$ time periods, and at each time period $t$, the demand of the product is…
Interactive behaviors are ubiquitous in modern cryptography, but are also present in $\lambda$-calculi, in the form of higher-order constructions. Traditionally, however, typed $\lambda$-calculi simply do not fit well into cryptography,…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
We define formally decohered quantum computers (using density matrices), and present a simulation of them by a probabalistic classical Turing Machine. We study the slowdown of the simulation for two cases: (1) sequential quantum computers,…
Inference-time scaling has emerged as a powerful way to improve large language model (LLM) performance by generating multiple candidate responses and selecting among them. However, existing work on dynamic allocation for test-time compute…
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…