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The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by selecting its state in a single step, considering all possible outcomes until the moment of selection. The system uses supertiles, each encoding the complete system being simulated. The universal system builds supertiles from its seed, each representing a single tile in Γ, transferring the information to simulate Γ to each new tile. Supertiles may also asynchronously transition states according to the rules of Γ. This result also implies IU for pairwise asynchronous Cellular Automata. 

For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Beyond what is contained in this brief announcement, we also investigate optimization variants of reachability, provide approximation results for maximizing species deletion, establish ETH-based lower bounds for NP-complete cases, and prove hardness for counting reaction sequences. 

This work fully characterizes fractal generation in the seeded Tile Automata model (seeded TA), a model similar to the abstract Tile Assembly model (aTAM) with the added ability for adjacent tiles to change states. Under these assumptions, we first show that all discrete self-similar fractals (DSSFs) with feasible generators are strictly buildable at scale 1 and temperature 1 in seeded TA. We then show that these results imply the existence of a single seeded TA system Γ that can strictly build any DSSF infinitely at scale 1 and temperature 1. 

Selective families of sets, or selectors, are combinatorial tools used to “isolate” individual members of sets from some set family. Given a set X and an element x ∈ X, to isolate x from X, at least one of the sets in the selector must intersect X on exactly x. We study (k,N)-permutation selectors which have the property that they can isolate each element of each k-element subset of {0, 1, ..., N − 1} in each possible order. These selectors can be used in protocols for ad-hoc radio networks to more efficiently disseminate informa- tion along multiple hops. In 2004, Gasieniec, Radzik and Xin gave a construc- tion of a (k, N )-permutation selector of size O(k2 log3 N ). This paper improves this by providing a probabilistic construction of a (k, N )-permutation selector of size O(k2 log N ). Remarkably, this matches the asymptotic bound for standard strong (k,N)-selectors, that isolate each element of each set of size k, but with no restriction on the order. We then show that the use of our (k, N )-permutation selector improves the best running time for gossiping in ad-hoc radio networks by a poly-logarithmic factor.