Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

Molecular Learning of a Soft-Disks Fluid

This work is based on the Equivalence between Molecular Dynamics and Neural networks. It provides learning proofs in a Lennard-Jones (LJ) fluid, presented as a network of particles having non-bonded interactions. I describe the fluid's learning as the property of an order that emerges as an adaptation in establishing equilibrium with energy and thermal conservation. The experimental section demonstrates the fluid can be trained with logic-gates patterns. The work goes beyond Molecular Computing's application, explaining how this model uses its intrinsic minimizing properties in learning and predicting outputs. Finally, it gives hints for a theory on real chemistry's computational universality.

Parallel Multiset Rewriting Systems with Distorted Rules

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

Life Worth Mentioning: Complexity in Life-Like Cellular Automata

Cellular automata (CA) have been lauded for their ability to generate complex global patterns from simple local rules. The late English mathematician, John Horton Conway, developed his illustrious Game of Life (Life) CA in 1970, which has since remained one of the most quintessential CA constructions—capable of producing a myriad of complex dynamic patterns and computational universality. Life and several other Life-like rules have been classified in the same group of aesthetically and dynamically interesting CA rules characterized by their complex behaviors. However, a rigorous quantitative comparison among similarly classified Life-like rules has not yet been fully established. Here we show that Life is capable of maintaining as much complexity as similar rules while remaining the most parsimonious. In other words, Life contains a consistent amount of complexity throughout its evolution, with the least number of rule conditions compared to other Life-like rules. We also found that the complexity of higher density Life-like rules, which themselves contain the Life rule as a subset, form a distinct concave density-complexity relationship whereby an optimal complexity candidate is proposed. Our results also support the notion that Life functions as the basic ingredient for cultivating the balance between structure and randomness to maintain complexity in 2D CA for low- and high-density regimes, especially over many iterations. This work highlights the genius of John Horton Conway and serves as a testament to his timeless marvel, which is referred to simply as: Life.

Breaking of the Trade-Off Principle between Computational Universality and Efficiency by Asynchronous Updating

Although natural and bioinspired computing has developed significantly, the relationship between the computational universality and efficiency beyond the Turing machine has not been studied in detail. Here, we investigate how asynchronous updating can contribute to the universal and efficient computation in cellular automata (CA). First, we define the computational universality and efficiency in CA and show that there is a trade-off relation between the universality and efficiency in CA implemented in synchronous updating. Second, we introduce asynchronous updating in CA and show that asynchronous updating can break the trade-off found in synchronous updating. Our finding spells out the significance of asynchronous updating or the timing of computation in robust and efficient computation.

Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices

What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction.

Quantum computational universality of hypergraph states with Pauli-X and Z basis measurements

Measurement-based quantum computing is one of the most promising quantum computing models. Although various universal resource states have been proposed so far, it was open whether only two Pauli bases are enough for both of universal measurement-based quantum computing and its verification. In this paper, we construct a universal hypergraph state that only requires X and Z-basis measurements for universal measurement-based quantum computing. We also show that universal measurement-based quantum computing on our hypergraph state can be verified in polynomial time using only X and Z-basis measurements. Furthermore, in order to demonstrate an advantage of our hypergraph state, we construct a verifiable blind quantum computing protocol that requires only X and Z-basis measurements for the client.

On Promoters/Inhibitors and Symport/Antiport with Traces in P Systems

This article brings together some rather powerful results on P systems in which the computation is performed by the communication of objects through symport and antiport rules considering the trace of an object through membranes, on the one hand, and by P systems with object-rewriting non-cooperative rules, promoters/inhibitors at the level of rules and only one catalyst, on the other. It is recalled here that computational universality can be reached whit these formalisms and that some of the proofs can be sketched. Three ideas are also put forward to brake the direct relationship (infinite hierarchy) induced by the size of the considered alphabet and the number of the membranes needed in a P system (with traces) to generate recursively enumerable languages on the chosen alphabet.

Phase Transition in Elementary Cellular Automata with Memory

We study elementary cellular automata with memory. The memory is a weighted function averaged over cell states in a time interval, with a varying factor which determines how strongly a cell's previous states contribute to the cell's present state. We classify selected cell-state transition functions based on Lempel–Ziv compressibility of space-time automaton configurations generated by these functions and the spectral analysis of their transitory behavior. We focus on rules 18, 22, and 54 because they exhibit the most intriguing behavior, including computational universality. We show that a complex behavior is observed near the nonmonotonous transition to null behavior (rules 18 and 54) or during the monotonic transition from chaotic to periodic behavior (rule 22).