Related papers: Compiling Turing Machines into Storage Modificatio…
We have developed the Model Master (MM) language for describing spreadsheets, and tools for converting MM programs to and from spreadsheets. The MM decompiler translates a spreadsheet into an MM program which gives a concise summary of its…
In many problems of supervised tensor learning (STL), real world data such as face images or MRI scans are naturally represented as matrices, which are also called as second order tensors. Most existing classifiers based on tensor…
We present algorithms to perform modular polynomial multiplication or modular dot product efficiently in a single machine word. We pack polynomials into integers and perform several modular operations with machine integer or floating point…
State space models (SSMs) are a powerful and widely-used class of probabilistic models for analysing time-series data across various fields, from econometrics to robotics. Despite their prevalence, existing software frameworks for SSMs…
A privacy-preserving Support Vector Machine (SVM) computing scheme is proposed in this paper. Cloud computing has been spreading in many fields. However, the cloud computing has some serious issues for end users, such as unauthorized use…
Clift and Murfet (2019) introduced a naive Bayesian smooth relaxation of Turing machines motivated by work in differential linear logic; this was subsequently used to endow spaces of program codes of bounded length with a smooth manifold…
The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…
Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…
This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…
Theory evaluation is a key problem in many areas: machine learning, scientific discovery, inverse engineering, decision making, software engineering, design, human sciences, etc. If we have a set of theories that are able to explain the…
A control model is typically classified into three forms: conceptual, mathematical and simulation (computer). This paper analyzes a conceptual modeling application with respect to an inventory management system. Today, most organizations…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
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…
Turing Machines (TMs) are the canonical model of computation in computer science and physics. We combine techniques from algorithmic information theory and stochastic thermodynamics to analyze the thermodynamic costs of TMs. We consider two…
For any fixed $k$, a remarkably simple single-tape Turing machine can simulate $k$ independent counters in real time. Informally, a counter is a storage unit that maintains a single integer (initially 0), incrementing it, decrementing it,…
Large language models have achieved remarkable success in time series prediction tasks, but their substantial computational and memory requirements limit deployment on lightweight platforms. In this paper, we propose the Symbolic Transition…
Machine learning (ML) models for code clone detection determine whether two pieces of code are semantically equivalent, which in turn is a key building block for software-engineering tasks like refactoring and security tasks like…
Chemputation reframes synthesis as the programmable execution of reaction code on a universally re-configurable hardware graph. Here we prove that a chemputer equipped with a finite, but extensible, set of reagents, catalysts and process…
Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…