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This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
There are enormous amount of examples of Computation in nature, exemplified across multiple species in biology. One crucial aim for these computations across all life forms their ability to learn and thereby increase the chance of their…
We study the problem of retrieval with instructions, where users of a retrieval system explicitly describe their intent along with their queries. We aim to develop a general-purpose task-aware retrieval system using multi-task instruction…
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…
A computational abstract machine based on two operations: referencing and bit copying is presented. These operations are sufficient for carrying out any computation. They can be used as the primitives for a Turing-complete programming…
In this paper, we propose a new concept called \textit{semantically equivalence} \wrt \textit{optimization phases} \textit{(\sep)}, which defines the set of programs a compiler considers semantically equivalent to the input using a set of…
Checking for Non-Termination (NT) of a given program P, i.e., determining if P has at least one non-terminating run, is an undecidable problem that continues to garner significant research attention. While unintended NT is common in…
This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…
The Unix terminal, or just simply, the terminal, can be found being applied in almost every facet of computing. It is available across all major platforms and often integrated into other applications. Due to its ubiquity, even marginal…
Alternatives to recurrent neural networks, in particular, architectures based on attention or convolutions, have been gaining momentum for processing input sequences. In spite of their relevance, the computational properties of these…
Recently, many techniques have been introduced that allow the (automated) classification of the runtime complexity of term rewrite systems (TRSs for short). In earlier work, the authors have shown that for confluent TRSs, innermost…
Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has…
We study when a programming language can emulate programs written in that same language without delegating the guest program back to the host evaluator or compiler. We call this property emulation-completeness. The central observation is…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
Recent progress in generative language models has enabled machines to generate astonishingly realistic texts. While there are many legitimate applications of such models, there is also a rising need to distinguish machine-generated texts…
Many important hyperproperties, such as refinement and generalized non-interference, fall into the class of $\forall\exists$ hyperproperties and require, for each execution trace of a system, the existence of another trace relating to the…
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions…
Because of the increasing demand for computation in DNN, researchers develope both hardware and software mechanisms to reduce the compute and memory burden. A widely adopted approach is to use mixed precision data types. However, it is hard…
Finding bugs is key to the correctness of compilers in wide use today. If the behaviour of a compiled program, as allowed by its architecture memory model, is not a behaviour of the source program under its source model, then there is a…
Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…