Related papers: Reactive Turing Machines
Redundancy is a fundamental characteristic of many biological processes such as those in the genetic, visual, muscular and nervous system; yet its function has not been fully understood. The conventional interpretation of redundancy is that…
Large language models (LLMs) increasingly rely on thinking models that externalize intermediate steps and allocate extra test-time compute, with think-twice strategies showing that a deliberate second pass can elicit stronger reasoning. In…
Life is confronted with computation problems in a variety of domains including animal behavior, single-cell behavior, and embryonic development. Yet we currently do not know of a naturally existing biological system that is capable of…
A Turmit is a Turing machine that works over a two-dimensional grid, that is, an agent that moves, reads and writes symbols over the cells of the grid. Its state is an arrow and, depending on the symbol that it reads, it turns to the left…
We propose a new implementation of the replica-exchange method (REM) in which replicas follow a pre-planned route in temperature space instead of a random walk. Our method satisfies the detailed balance condition in the proposed route. The…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent in their…
Exact inference in complex probabilistic models often incurs prohibitive computational costs. This challenge is particularly acute for autonomous agents in dynamic environments that require frequent, real-time belief updates. Existing…
The Transformer architecture has become the de facto standard for Large Language Models (LLMs), demonstrating remarkable capabilities in language understanding and generation. However, its application in conversational AI is fundamentally…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
We show that alternating Turing machines, with a novel and natural definition of acceptance, accept precisely the inductive (Pi-1-1) languages. Total alternating machines, that either accept or reject each input, accept precisely the…
Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions. However, RNNs usually suffer from the issues of vanishing and exploding gradients in standard RNN…
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…
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to…
In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…