A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [26] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated quantum-algorithmically by various forms of quantum automata families (including 1qqaf's). We study an efficient way to accomplish certain machine learning tasks by training these AEQSs quantumly. When AEQSs are controlled by 1qqaf's, it suffices in essence to find an optimal 1qqaf that approximately solves a target relational problem. For this purpose, we develop a basic idea of approximately utilizing well-known quantum algorithms for quantum counting, quantum amplitude estimation, and quantum approximation. We then provide a rough estimation of the efficiency of our quantum learning algorithms for AEQSs.
This paper studies the effects of interactivity on molecular computation, specifically in the Step Chemical Reaction Networks model (Step CRNs), by adding the ability for a user to interact with the system by selecting which species to add at each step, or by having some control over which reactions execute. The two proposed variants are Interactive CRNs and Randomized Interactive CRNs. We show that in Interactive CRNs, even when restricted to void (deletion-only) rules of relatively small size, if a user can decide which species to add at each step based on the configuration, reachability is PSPACE-complete when bounded and EXPTIME-hard when unbounded. In Randomized Interactive CRNs, we prove that reachability with void rules is PSPACE-complete.
We introduce a framework that connects two discrete models of natural computing, cellular automata (CA) and reaction systems (RS). We define pattern graphs of a CA as one-out digraphs where vertices correspond to totally periodic configurations and edges reflect CA evolution. Using pattern graphs based on periodic configurations we show that every one-dimensional binary CA can be transformed into an RS via its zero-context graph and provide counterexamples for the converse. Modified techniques, such as increasing the number of states and subgraphs of pattern graphs, are used to transform arbitrary RS into CA.
The extraction of features from speech is the most critical process in speech signal processing. Mel Frequency Cepstral Coefficients (MFCC) are the most widely used features in the majority of the speaker and speech recognition applications, as the filtering in this feature is similar to the filtering taking place in the human ear. But the current MFCC extraction is complex and requires time-frequency translations. Through our investigation, we were able to model a reservoir as a feature extractor capable of extracting the Mel Frequency Cepstral Coefficient (MFCC) without time-frequency domain translations. We have developed a real-time audio signal processing system by simplifying audio signal processing through the utilization of reservoir computers, which are significantly easier to train. We have established an experimental framework for end-to-end audio processing utilizing the reservoir and have investigated its capability to perform end-to-end audio signal processing.
This study demonstrates how to provide specific guarantees on the entropy produced by quantum circuits implementing Boolean functions. More specifically, we study guarantees on von Neumann entropy for subsystems in such circuits. Our findings indicate that input state initialization by rotating the target qubit around the X -axis of the Bloch sphere, combined with arbitrary but fixed individual qubit rotations of the control qubits around any axis or a combination of thereof, preserves the von Neumann entropy of reduced density matrices across subsystem traces. In contrast, similar rotations around the Y -axis cause entropy variation with rotation angle. Moreover, ceteris paribus, arbitrary qubit rotations on all qubits, including the target, result similarly in variability of subsystem entropy. We apply these findings to secure the classical communication channel in a novel multi-qubit quantum teleportation protocol. We depict a full IBM Qiskit implementation and its corresponding graphical-empirical example for the execution of a three-qubit quantum teleportation protocol. Overall, our results reveal insights into system entanglement and demonstrate that Boolean functions provide a structured approach for the purposes of controlling the dynamics of quantum entropy. This has implications beyond the secure obfuscation of classical communication in quantum teleportation and warrants additional investigation of quantum Boolean functions in the broad context of quantum information scrambling and beyond.
We consider Additive CA on a finite group, also called Group CA. First of all, we present the abelian situation in which easy-to-check algebraic characterizations of the main dynamical properties in terms of the CA local rule have been provided. Then, we move to the non abelian scenario. Precisely, we consider the dynamical behavior of Additive CA on a number of classes of specific finite groups and for each of those classes, we focus our attention to the non abelian scenarios, providing exact characterizations for some dynamical properties.
This short paper presents the initial investigation of the biologically inspired coherent spin dynamics for use in an unconventional in-materio computing scenario. The radical pair mechanism is analyzed from the information-theoretic perspective based on the previously developed framework and further investigated regarding the structure of multivariate information, an approach recently adopted for describing emergent phenomena. Some initial simulation results indicate that the entropic relations within the investigated system hold for the addressed framework. This knowledge provides directions for manipulation of physical substrates with radical pairs toward a computational goal.
Echo State Networks (ESNs) are stated in literature to use a random structure to project an input sequence into a higher dimensional space where the input becomes linearly separable. However, the linear mathematics used for this projection are incapable of increasing the dimensionality of the input, and the commonly used tanh () activation function tends not to produce much nonlinearity. Therefore, any increase in dimensionality is due to the echoes of the ESN. We introduce Lagged Input Regression Computation to investigate what types of ESN can be replaced with simpler non-randomised structures. We show that tanh () -based ESNs behave as simple linear memory systems, whereas LeakyReLU provides a more effective non-linearity. We also show that the use of certain orthogonal polynomials in defining nonlinear memory capacity benchmarks gives a misleading impression of nonlinearity, due to the relevant high order polynomials nevertheless containing a linear term.
Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. In 2022, Alhazov et al. introduced time-varying systems as a restriction of GCID systems; in these systems, the components are cyclically ordered. A rule is applied to a string in a component and the resultant string moves to the next component as specified by this order. The language of the system is the set of all terminal strings collected in a distinguished component that is both the initial and the final one. With this restriction, we obtain several new computational completeness results for some typical descriptional complexity measures well-studied in the area of GCID systems.
We have created a new card game, Gakmoro, where two players each have seven cards numbered from 1 to 7. In each round, they secretly choose one to three cards to compete based on their total value; the first player to win two rounds wins the game. The unique feature of Gakmoro is that the cards chosen by the players must remain secret, and only the winner of each round is revealed. This secrecy is expected to add depth to the game by emphasizing the strategy of reading an opponent’s hand. As designed, the game requires a dealer to secretly calculate the sum of the cards and announce only the winner. In this paper, instead of relying on a human dealer, we use card-based cryptography to virtually fulfill the dealer’s role. In other words, we design an ‘unconventional’ computation protocol that allows players to securely determine the winner without a dealer using a physical deck of cards.
This short paper is about the behavior of the cellular automaton (CA) obtained by the composition of two or more cellular automata. The general question we aim to face is: what is the relationship between a certain property of the CA obtained by the composition and the same (or other) property of each single CA appearing in the composition? We show that if P is one of the main basic and set-theoretic properties, the CA resulting from the composition has a certain property P iff both CA components have P, while this equivalence generally no longer holds when P is one of the main dynamical properties. Some important questions naturally arise from these results.
A common representation of crystal structures is by periodic graphs, i.e., graphs whose automorphism groups have subgroups of translational symmetries. Such graphs may be represented as (finite) quotient graphs (called voltage graphs) whose edges are labeled by corresponding elements of their translational subgroup. We outline a polynomial time algorithm for determining whether two finite bi-deterministically edge-labeled voltage graphs with voltages from corresponding translational subgroups generate isomorphic periodic graphs. This algorithm aids in the classification of crystal structures and provides a method for determining whether two sets of building blocks can assemble isomorphic crystals.
This paper describes an efficient variation of a well-known technique for converting a general-purpose analog computer (GPAC) to a chemical reaction network (CRN). If an input system has n variables, the existing dual-railing technique requires 2n variables in the resulting system. As the resulting CRNs are often fed into downstream processes which may themselves be exponential in the number of variables [7], it is frequently worthwhile to try to minimize the number of variables generated in this conversion. This paper presents a technique that results in fewer than n new variables, by rewriting only those whose positive terms are ‘infected’ by ill-formed variables.
Spiking Neural Networks (SNNs) offer a biologically inspired approach to modeling neuronal computation, emphasizing timed latency and probabilistic activation over the numerical computations typical of traditional deep-learning models. This paper introduces a modeling framework for SNNs that incorporates the RP-LI F (Refractory-evolve Probabilistic Leaky Integrate-and-Fire) neuron model to capture realistic neuronal dynamics. We present a prototype, SuNNy, to translate elementary neural bundles and their synaptic connections into formal models compatible with PRISM, enabling model checking of stochastic timing properties using Probabilistic Computation Tree Logic (PCTL). Additionally, our framework integrates with Nengo for simulation, allowing for experimentation on large-scale SNNs. A key challenge addressed is the study of how compound SNN models can meet global reaction requirements based on the stochastic behaviors of individual neural bundles. While the framework supports parametric variations to represent different neuronal states, this work focuses on the core modeling, verification, and simulation techniques. Specific applications, such as simulating impaired neurons, are not explored in this paper but are left for future research. Our approach provides a foundation for both formal verification and simulation of SNNs, bridging the gap between theoretical models and practical tools for analyzing neuronal computations.
We investigate the computational power of Step-Cycle Chemical Reaction Networks (CRNs) when restricted to void reactions of size at most (3, 1). Step-Cycle CRNs extend the previously introduced step CRN model by repeatedly cycling through a fixed sequence of species additions and reaction phases. We show that even under the severe constraint of trimolecular void rules—which can only delete or preserve species—the model retains full computational power. In particular, we prove that (3,1) void Step-Cycle CRNs can polynomially simulate (1) any general CRN, (2) any general Step CRN, and (3) any general Step-Cycle CRN. Ultimately, these results demonstrate that the Step-Cycle model retains its complete expressive power even when restricted to (3, 1)-size void rules.
Classical Cellular Automata (CCAs) are a powerful computational framework widely used to model complex systems driven by local interactions. Their simplicity lies in the use of a finite set of states and a uniform local rule, yet this simplicity leads to rich and diverse dynamical behaviors. CCAs have found applications in numerous scientific fields, including quantum computing, biology, social sciences, and cryptography. However, traditional CCAs assume complete certainty in the state of all cells, which limits their ability to model systems with inherent uncertainty. This paper introduces a novel generalization of CCAs, termed Cellular Automata on spaces of probability Measures (CAMs), which extends the classical framework to incorporate probabilistic uncertainty. In this setting, the state of each cell is described by a probability measure, and the local rule operates on configurations of such probability measures. This study lays the groundwork for future exploration of CAMs, offering a flexible and robust framework for modeling uncertainty in cellular automata and opening new directions for both theoretical analysis and practical applications.
Central Pattern Generators (CPGs) are neural circuits capable of autonomously producing rhythmic output patterns without requiring rhythmic input. They maintain stable phase relationships among constituent oscillators, adapt to sensory feedback and descending modulation, and exhibit resilience to perturbations. This work presents a novel hybrid Analog-Digital CPG architecture that leverages the continuous, low-latency dynamics of analog oscillators alongside the flexibility, reconfigurability, and precision of digital control. The proposed system features tunable parameters and a modular design, enabling real-time adaptation to sensory inputs and environmental conditions. This approach provides a versatile framework for generating robust, adaptable gait patterns, with applications spanning autonomous robotics, soft robotics, and human-assistive technologies.
We consider 2-state reversible gates that route tokens from input wires to output wires. This can be thought of as a model that reduces computation to just flow control, with wires representing execution paths, and the token representing the current execution point. Memory and computation are strictly co-localized, in the sense that the state of a gate is only changeable or observable by a token that passes through it. Also known as Reversible Logic Elements with Memory (RLEMs), such gates have been studied extensively by Kenichi Morita and his co-authors. Through a series of surprising results, they have shown that all non-degenerate 2-state RLEMs with 3 or more inputs are universal, meaning any of them can be used to build any other RLEM of any size and number of states. They also proved that all smaller (2 or fewer inputs) 2-state RLEMs are not universal, with the exception of one gate that defied analysis. This one remaining gate, known as 2-17, was conjectured to also be non-universal, but this has remained an open question since 2012. Here we resolve this open question by showing that this extremely simple gate is in fact universal. This makes it the smallest universal reversible gate, and we name it the Morita gate in honor of Morita’s extensive foundational work in this area.
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of non-coding RNAs. Recent developments in sequencing technology and artificial intelligence have yielded numerous biological data that can be represented with tree structures. This requires novel methods for tree structure data analytics. Tree polynomials provide a computationally efficient, interpretable and comprehensive way to encode tree structures as matrices, which are compatible with most data analytics tools. Machine learning methods based on the Canberra distance between tree polynomials have been introduced to analyze phylogenies and nucleic acid structures. In this paper, we compare the performance of different distances in tree clustering methods based on a tree distinguishing polynomial. We also implement two basic autoencoder models for clustering trees using the polynomial. We find that the distance based methods with entry-level normalized distances have the highest clustering accuracy among the compared methods.
Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We examine what properties of uniform CA can be recovered by restricting the rule distribution to be (uniformly) recurrent, focusing on only 1D NUCA. We show that a bijective NUCA with a uniformly recurrent rule distribution is reversible. We also show that if a NUCA is surjective and has a recurrent rule distribution, or if it is bijective, then it is balanced. We present an example of a NUCA which has a non-empty and non-residual set of equicontinuity points, and one which is not sensitive but has no equicontinuity points. Finally, we show that (positively) expansive NUCA are sensitive.
