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Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
Nanomechanical computers promise a greatly improved energetic efficiency compared to their electrical counterparts. However, progress towards this goal is hindered by a lack of modular components, such as logic gates or transistors, and…
In this paper we provide a practical demonstration of how the modularity in a Behavior Tree (BT) decreases the effort in programming a robot task when compared to a Finite State Machine (FSM). In recent years the way to represent a task…
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…
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…
We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time…
We show that a quantum state can be perfectly cloned up to global mirroring with a unitary transformation that depends on one single parameter. We then show that this is equivalent to "perfect" cloning for quantum associative memories…
Recent works have independently suggested that Quantum Mechanics might permit for procedures that transcend the power of Turing Machines as well as of `standard' Quantum Computers. These approaches rely on and indicate that Quantum…
The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases.…
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…
Functional MRI (fMRI) is crucial for studying brain function and diagnosing neurological disorders. However, existing analysis methods suffer from reproducibility and transferability challenges due to complex preprocessing pipelines and…
We specify a second-order type system $\mathbf{F}_2^\mu$ that is tailored for representing nonterminations. The nonterminating trace of a term $t$ in a rewrite system $\mathcal{R}$ corresponds to a productive inhabitant $e$ such that…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
In this paper we introduce a fuzzy version of symport/antiport membrane systems. Our fuzzy membrane systems handle possibly inexact copies of reactives and their rules are endowed with threshold functions that determine whether a rule can…
This paper introduces a special type of systems, defines their properties, and then demonstrates that a reduction machine for pure untyped extensional lambda calculus can be implemented as a system of the introduced type. Specifically, we…
The Neural Turing Machine (NTM) is more expressive than all previously considered models because of its external memory. It can be viewed as a broader effort to use abstract external Interfaces and to learn a parametric model that interacts…
Finite state machines are widely used as a sound mathematical formalism that appropriately describes large scale, distributed and complex systems. Multiple interactions of finite state machines in complex systems are well captured by the…
Recently, developing an automatic reading system for analog measuring instruments has gained increased attention, as it enables the collection of numerous state of equipment. Nonetheless, two major obstacles still obstruct its deployment to…