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In this paper we study complexities for the multiple-handed tile self-assembly model, a generalization of the two-handed tile assembly model in which assembly proceeds by repeatedly combining up to h assemblies together into larger assemblies. We ...${}_{}$$\frac{}{}$$\mathcal{}\mathrm{}$$$$\mathcal{}\mathrm{}$$\mathcal{}$

Inspired by the nonlinear dynamics of neural networks, new unconventional computing hardware has emerged under the name of physical reservoir computing. In this paradigm, an input-driven dynamical system (the reservoir) is exploited and trained to ...

Recent research into analog computing has introduced new notions of computing real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion of computing real numbers in real-time with chemical reaction networks (CRNs), introducing the ...${\mathbb{}}_{}$${\mathbb{}}_{}$${\mathbb{}}_{}{\mathbb{}}_{}$${\mathbb{}}_{}$${\mathbb{}}_{}{\mathbb{}}_{}$

Cryptarithmetic, also known as Verbal Arithmetic or Word Addition, is a popular pencil puzzle in which the aim is to deduce which letter corresponds to which numeral, given a mathematical equation in which each numeral (from 0 to 9) has been ...

We consider the recognition problem of the Dyck Language generalized for multiple types of brackets. We provide an algorithm with quantum query complexity $O(\sqrt{n}{(logn)}^{0.5k})$, where n is the length of input and k is the maximal nesting depth of ...$\sqrt{}{}^{}$

We initiate the study of the verification power of Affine finite automata (AfA) as a part of Arthur-Merlin (AM) proof systems. We show that every unary language is verified by a real-valued AfA verifier. Then, we focus on the verifiers restricted ...

A string assembling system is a generative model that generates strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower ...

In this paper, we investigate the power of systems in the abstract Tile Assembly Model to self-assemble shapes having fractal dimensions between 1 and 2. We introduce a concept of sparsity as a tool for investigating such systems and demonstrate ...

Ising machines have been attracting attention due to their ability to use mixed discrete/continuous mechanisms to solve difficult combinatorial optimization problems. We present BLIM, a novel Ising machine scheme that uses latches (bistable ...

An undirected graph G is known to both the prover P and the verifier V, but only P knows a subgraph H of G. Without revealing any information about H, P wants to convince V that H is a connected spanning subgraph of G, i.e. H is connected and ...

The Echo State Network reservoir computing model is used in many applications. The original equations have a form of ‘instantaneous’ information flow. Here we suggest using a more physically realistic form of the equations, which takes into ...

The logical depth of a piece of data has served as a complexity measure to describe the amount of “usefulness” and “non-randomness” of information stored in the data itself, which is originated from Kolmogorov complexity. This notion of logical ...