24 papers · ranked by Valyu relevance
Nick Zhang
If Turing's groundbreaking paper [21] in 1936 laid the foundation of the theory of computation (ToC), it is no exaggeration to say that Cook's paper in 1971, "The complexity of theorem proving procedures" [4] has pioneered the study of computational complexity. So computational complexity, as an independent research…
Danupon Nanongkai, Michele Scquizzato
The Massively Parallel Computation (MPC) model serves as a common abstraction of many modern large-scale data processing frameworks, and has been receiving increasingly more attention over the past few years, especially in the context of classical graph problems. So far, the only way to argue lower bounds for this…
Andrew N. Sloss
Algorithms are becoming more capable, and with that comes hic sunt dracones ("here be dragons"). The term symbolizes areas beyond our known maps. We use this term since we are stepping into an exciting, potentially dangerous, and unknown area with algorithms. Our curiosity to understand the natural world drives our…
Tao Hong, William R. Stauffer
Economic deliberations are slow, effortful and intentional searches for solutions to difficult economic problems. Although such deliberations are critical for making sound decisions, the underlying reasoning strategies and neurobiological substrates remain poorly understood. Here two nonhuman primates performed a…
Chuyu Xiong
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big question: Is there a better way to deal with these highly complex problems other…
Héctor Zenil
At the intersection of what I call uncomputable art and computational epistemology, a form of experimental philosophy, we find a most exciting and promising areas of science related to causation with an alternative, possibly best possible, solution to the challenge of the inverse problem. That is, the problem of…
Christopher P. Kempes, Michael Lachmann, Andrew Iannaccone, G. Matthew Fricke + 3 more
'G. Matthew Fricke' 'M. Redwan Chowdhury' 'Sara I. Walker' 'Leroy Cronin'] Assembly theory (AT) quantifies selection using the assembly equation, identifying complex objects through the assembly index, the minimal steps required to build an object from basic parts, and copy number, the observed instances of the object.…
Anurag Dutta, K. Lakshmanan, John Harshith, Aditya Ramamoorthy
—Time Complexity is an important metric to compare algorithms based on their cardinality. The commonly used, trivial notations to qualify the same are the Big-Oh, Big-Omega, Big-Theta, Small-Oh, and Small-Omega Notations. All of them, consider time a part of the real entity, i.e., Time coincides with the horizontal…
Tao Hong, William R. Stauffer
Complex economic decisions are often combinatorial: they require individuals to select from many alternatives under strict constraints on time, resources, and energy. Combinatorial reasoning is the cognitive process that enables decision makers to construct and evaluate multiple potential solutions in the face of these…
Raffaele Marino
This chapter delves into the realm of computational complexity, exploring the world of challenging combinatorial problems and their ties with statistical physics. Our exploration starts by delving deep into the foundations of combinatorial challenges, emphasizing their nature. We will traverse the class P, which…
Tiasa Mondol, Daniel G. Brown, Ercan Kuruoglu
We build an analysis based on the Algorithmic Information Theory of computational creativity and extend it to revisit computational aesthetics, thereby, improving on the existing efforts of its formulation. We discuss Kolmogorov complexity, models and randomness deficiency (which is a measure of how much a model falls…
Anamika Agrawal, Michael A. Buice
The simple linear threshold units used in many artificial neural networks have a limited computational capacity. Famously, a single unit cannot handle non-linearly separable problems like XOR. In contrast, real neurons exhibit complex morphologies as well as active dendritic integration, suggesting that their…
Zoe Leyva-Acosta, Eduardo Acuña Yeomans, Francisco Hernandez-Quiroz, Boris Ryabko
'Boris Ryabko'] We study practical approximations of Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is designed to address…
Authors not listed
The era of exascale computing presents both exciting opportunities and unique challenges for quantum mechanical simulations. While the transition from petaflops to exascale computing has been marked by a steady increase in computational power, the shift towards heterogeneous architectures, particularly the dominant…
Juan Prada, Johannes Balkenhol, Özge Osmanoglu, Maral Afshar + 6 more
Decisions in biology happen fast and are driven by evolution to optimize survival chances. In platelets, this is achieved by organizing signaling cascades into rapid decision-funnels with modulatory crosstalk. We show that network decision processes underlying cellular decisions are tough to solve (equivalent to…
Eugene Christo V R, Christoph Robert Meinecke, Bert Nitzsche, Roman Lyttleton + 5 more
Network-based biocomputing (NBC) presents an energy-efficient, parallel computing approach for solving nondeterministic polynomial time (NP) complete problems by leveraging motor-driven cytoskeletal filaments that explore all possible solutions through nanofabricated networks in a massively parallel fashion. However…
Kamal Dingle, Pascal Hagolani, Roland Zimm, Muhammad Umar + 2 more
By linking genetic sequences to phenotypic traits, genotype-phenotype maps represent a key layer in biological organisation. Their structure modulates the effects of genetic mutations, shaping evolutionary outcomes. Recent work based on algorithmic information theory introduced an upper bound on the likelihood of a…
Ido Aizenbud, David Beniaguev, Noam Pnueli, Idan Segev + 1 more
Cortical pyramidal neurons possess elaborate dendritic trees with diverse nonlinear membrane conductances and thousands of plastic synapses, suggesting substantial computational capabilities at the single-cell level. Yet, what can a neuron compute remains an open question, largely due to the lack of a systematic…
Ruben Sanchez-Garcia, Dávid Havasi, Gergely Takács, Matthew C. Robinson + 3 more
Compound availability is a critical property for design prioritization across the drug discovery pipeline. Historically, and despite their multiple limitations, compound-oriented synthetic accessibility scores have been used as proxies for this problem. However, the size of the catalogues of commercially available…
Authors not listed
The Hidden Subgroup Problem (HSP) unifies several landmark quantum algorithms, yet systematic exploration of its variants and modern applications has slowed. This paper revives HSP-based algorithm design by examining new group structures with direct relevance to post-quantum cryptography, lattice problems, and…
Davide Rattacaso, Daniel Jaschke, Marco Ballarin, Ilaria Siloi + 1 more
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent expressions with increasing problem size. We introduce quantum normal form reduction…
Ruben Sanchez-Garcia, Dávid Havasi, Gergely Takács, Matthew C. Robinson + 3 more
Compound availability is a critical property for design prioritization across the drug discovery pipeline. Historically, and despite their multiple limitations, compound-oriented synthetic accessibility scores have been used as proxies for this problem. However, the size of the catalogues of commercially available…
Authors not listed
Step-by-step thinking is essential in all domains of chemical sciences and engineering. While machine learning tools are broadly used, algorithms that automate reasoning are far less common. We elaborate on seven categories of human reasoning activities and connect each to applications in chemical science and…
Authors not listed
This work establishes theoretical foundations for hierarchical quantum-classical algorithm design, where complex problems are decomposed across multiple spatial, temporal, or organizational scales with quantum and classical computation assigned to appropriate levels. We develop a mathematical framework that…