Related papers: Complete Simulation of Automata Networks
An Abstract Graph Machine(AGM) is an abstract model for distributed memory parallel stabilizing graph algorithms. A stabilizing algorithm starts from a particular initial state and goes through series of different state changes until it…
We consider the task of computing functions $f: \mathbb{N}^k\to \mathbb{N}$, where $ \mathbb{N}$ is the set of natural numbers, by finite teams of agents modelled as deterministic finite automata. The computation is carried out in a…
Generalized finite automata (GFAs), probabilistic finite automata (PFAs), and one-way general quantum finite automata (1gQFA) recognize the same strict-cutpoint languages, but the state complexity of exact probabilistic simulation has…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
We consider Parallel Random Access Machine (PRAM) which has some processors and memory cells faulty. The faults considered are static, i.e., once the machine starts to operate, the operational/faulty status of PRAM components does not…
Machine Learning (ML)-based network models provide fast and accurate predictions for complex network behaviors but require substantial training data. Collecting such data from real networks is often costly and limited, especially for…
The life of the modern world essentially depends on the work of the large artificial homogeneous networks, such as wired and wireless communication systems, networks of roads and pipelines. The support of their effective continuous…
Experimental studies of synthetic quantum matter are necessarily restricted to approximate ground states prepared on finite-size quantum simulators. In general, this limits their reliability for strongly correlated systems, for instance, in…
We perform a tensor network simulation of the (1+1)-dimensional $O(3)$ nonlinear $\sigma$-model with $\theta=\pi$ term. Within the Hamiltonian formulation, this field theory emerges as the finite-temperature partition function of a modified…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
An approximate program transformation is a transformation that can change the semantics of a program within a specified empirical error bound. Such transformations have wide applications: they can decrease computation time, power…
This chapter is concerned with the design and analysis of algorithms for minimizing finite automata. Getting a minimal automaton is a fundamental issue in the use and implementation of finite automata tools in frameworks like text…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
The transformer has revolutionized modern AI across language, vision, and beyond. It consists of $L$ layers, each running $H$ attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input…
Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum…
Simulation code for conventional supercomputers serves as a reference for neuromorphic computing systems. The present bottleneck of distributed large-scale spiking neuronal network simulations is the communication between compute nodes.…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
Quantum computation based on quantum cellular automata (QCA) can greatly reduce the control and precision necessary for experimental implementations of quantum information processing. A QCA system consists of a few species of qubits in…
Let $\mathbb{K}$ be a finite commutative ring, and let $\mathbb{L}$ be a commutative $\mathbb{K}$-algebra. Let $A$ and $B$ be two $n \times n$-matrices over $\mathbb{L}$ that have the same characteristic polynomial. The main result of this…
Measurement data is often sampled irregularly i.e. not on equidistant time grids. This is also true for Hamiltonian systems. However, existing machine learning methods, which learn symplectic integrators, such as SympNets [20] and…