This work presents a new class of reaction automata, called Chemical Pure Reaction Automata (CPRA). CPRA combines characteristics of chemical reaction automata, as introduced by Okubo et al. in 2016, with those of the more recently defined pure reaction automata. Unlike standard chemical reaction automata, CPRA lack permanence, meaning their result states consist solely of the reaction products, with unconsumed reactants being discarded. We investigate the computational power of two CPRA variants, both working in a maximally parallel manner. We first prove that deterministic CPRA (DCPRA)—in which at every state, for each input symbol, the resulting state is the same for all multisets of enabled reactions—are not Turing complete. We then show that non-deterministic CPRA are Turing complete and thus strictly more powerful than DCPRA: namely, the set of languages accepted by CPRA in the maximally parallel manner contains the set of languages accepted by standard chemical reaction automata in the same manner.

This work introduces the new class of pure reaction automata, as well as a new update manner, called maximal reactive manner, that can also be applied to standard reaction automata. Pure reaction automata differ from the standard model in that they don’t have permanence: the entities that are not consumed by the reactions happening at a certain state are not conserved in the result states. We prove that the set of languages accepted by the new class under the maximal reactive manner contains the set of languages accepted by standard reaction automata under the same manner or under the maximal parallel manner. We also prove that a strict subclass of pure reaction automata can compute any partial recursive function.

Reaction systems are discrete dynamical systems that simulate biological processes within living cells through finite sets of reactants, inhibitors, and products. In this paper, we study the computational complexity of deciding on the existence of fixed points and attractors in the restricted class of additive reaction systems, in which each reaction involves at most one reactant and no inhibitors. We prove that all the considered problems, that are known to be hard for other classes of reaction systems, are polynomially solvable in additive systems. To arrive at these results, we provide several non-trivial reductions to problems on a polynomially computable graph representation of reaction systems that might prove useful for addressing other related problems in the future.

Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems related to the existence of fixed points and attractors in two constrained classes of reaction systems, in which either reactants or inhibitors are disallowed. These problems have biological relevance and have been extensively studied in the unconstrained case; however, they remain unexplored in the context of reactantless or inhibitorless systems. Interestingly, we demonstrate that although the absence of reactants or inhibitors simplifies the system's dynamics, it does not always lead to a reduction in the complexity of the considered problems.

Elastic Degenerate (ED) strings and Elastic Founder (EF) graphs are two versions of acyclic components of pangenomes. Both ED strings and EF graphs (which we collectively name variable strings) extend the well-known notion of indeterminate string. Recent work has extensively investigated algorithmic tasks over these structures, and over several other variable strings notions that they generalise. Among such tasks, the basic operation of matching a pattern into a text, which can serve as a toolkit for many pangenomic data analyses using these data structures, deserves special attention. In this paper we: (1) highlight a clear taxonomy within both ED strings and EF graphs ranging through variable strings of all types, from the linear string up to the most general one; (2) investigate the problem PVART(X, Y) of matching a solid or variable pattern of type X into a variable text of type Y; (3) using as a reference the quadratic conditional lower bounds that are known for PVART(SOLID,ED) and PVART(SOLID,EF), for all possible types of variable strings X and Y we either prove the quadratic conditional lower bound for PVART(X, Y), or provide non-trivial, often sub-quadratic, upper bounds, also exploiting the above-mentioned taxonomy.