Related papers: Computing in permutation groups without memory
Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
We introduce a general scheme for sequential one-way quantum computation where static systems with long-living quantum coherence (memories) interact with moving systems that may possess very short coherence times. Both the generation of the…
This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…
Most neural networks utilize the same amount of compute for every example independent of the inherent complexity of the input. Further, methods that adapt the amount of computation to the example focus on finding a fixed inference-time…
A permutation code is a nonlinear code whose codewords are permutation of a set of symbols. We consider the use of permutation code in the deletion channel, and consider the symbol-invariant error model, meaning that the values of the…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The…
Permutation is the different arrangements that can be made with a given number of things taking some or all of them at a time. The notation P(n,r) is used to denote the number of permutations of n things taken r at a time. Permutation is…
Two completely new algorithms for generating permutations, shift-cursor algorithm and level algorithm, and their efficient implementations are presented in this paper. One implementation of the shift cursor algorithm gives an optimal…
We describe a complete Scheme implementation of miniAdapton, which implements the core functionality of the Adapton system for incremental computation (also known as self-adjusting computation). Like Adapton, miniAdapton allows programmers…
In recent years, the energy consumption of computing systems has increased and a large fraction of this energy is consumed in main memory. Towards this, researchers have proposed use of non-volatile memory, such as phase change memory…
Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the…
Forgetting - or variable elimination - is an operation that allows the removal, from a knowledge base, of middle variables no longer deemed relevant. In recent years, many different approaches for forgetting in Answer Set Programming have…
Clustering is a crucial tool for analyzing data in virtually every scientific and engineering discipline. There are more scalable solutions framed to enable time and space clustering for the future large-scale data analyses. As a result,…
Long Short-Term Memory (LSTM) is a special class of recurrent neural network, which has shown remarkable successes in processing sequential data. The typical architecture of an LSTM involves a set of states and gates: the states retain…
In this paper, we look at the complexity of designing algorithms without any bank conflicts in the shared memory of Graphical Processing Units (GPUs). Given input of size $n$, $w$ processors and $w$ memory banks, we study three fundamental…
Transformer models gain popularity because of their superior inference accuracy and inference throughput. However, the transformer is computation-intensive, causing a long inference time. The existing works on transformer inference…
Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize…
Large language models (LLMs) have recently transformed natural language processing, enabling machines to generate human-like text and engage in meaningful conversations. This development necessitates speed, efficiency, and accessibility in…
This note presents a non-associative algebraic framework for the representation and computation of information items in high-dimensional space. This framework is consistent with the principles of spatial computing and with the empirical…