Related papers: On the Holographic Geometry of Deterministic Compu…
We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations. This model of computation is a natural generalization of several…
Hirschberg's algorithm (1975) reduces the space complexity for the longest common subsequence problem from $O(N^2)$ to $O(N)$ via recursive midpoint bisection on a grid dynamic program (DP). We show that the underlying idea generalizes to a…
Deterministic routing has emerged as a promising technology for future non-terrestrial networks (NTNs), offering the potential to enhance service performance and optimize resource utilization. However, the dynamic nature of network topology…
Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that…
Online algorithms make decisions based on past inputs. In general, the decision may depend on the entire history of inputs. If many computers run the same online algorithm with the same input stream but are started at different times, they…
Dynamic programming on various graph decompositions is one of the most fundamental techniques used in parameterized complexity. Unfortunately, even if we consider concepts as simple as path or tree decompositions, such dynamic programming…
Poor time predictability of multicore processors has been a long-standing challenge in the real-time systems community. In this paper, we make a case that a fundamental problem that prevents efficient and predictable real-time computing on…
In this paper, we show that for one sign of the deformation coupling single-trace $T{\bar T}$ deformation moves the holographic screen in G\"{o}del universe radially inward. For the other sign of the coupling it moves the holographic screen…
Deterministic finite automata are one of the simplest and most practical models of computation studied in automata theory. Their conceptual extension is the non-deterministic finite automata which also have plenty of applications. In this…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
We show that the compressed suffix array and the compressed suffix tree of a string $T$ can be built in $O(n)$ deterministic time using $O(n\log\sigma)$ bits of space, where $n$ is the string length and $\sigma$ is the alphabet size.…
An emerging generative artificial intelligence (AI) based on neural networks starts to grow in popularity with a revolutionizing capability of creating new and original content. As giant generative models with millions to billions of…
Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…
We present a computation model based on a subclass of GP 2 graph programs which can simulate any off-line Turing machine of space complexity O(s(n) log s(n)) in space O(s(n)). The simulation only requires a quadratic time overhead. Our…
We employ a deep learning method to deduce the \textit{bulk} spacetime from \textit{boundary} optical conductivity. We apply the neural ordinary differential equation technique, tailored for continuous functions such as the metric, to the…
There exists a remarkable four-qutrit state that carries absolute maximal entanglement in all its partitions. Employing this state, we construct a tensor network that delivers a holographic many body state, the H-code, where the physical…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
Gravity is uniquely situated in between classical topological field theories and standard local field theories. This can be seen in the the quasi-local nature of gravitational observables, but is nowhere more apparent than in gravity's…
When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a…