We investigate the relationship of languages characterized by variants of string assembling systems and by Watson-Crick automata with a small number of states. Besides the general variant, we consider so-called free and pure string assembling systems, and compare their language generating power to Watson-Crick automata having one, two, or three states in their state sets. In some cases, restricted variants of the models describing unary languages are also considered.
Graph-controlled insertion-deletion (GCID) systems are regulated extensions of insertion-deletion systems. At AFL 2023, we introduced star-controlled GCID systems as a restriction of GCID systems where there is a special component, namely, a central component that will process the string and then send it to any other component that processes another step and then send the string back to the central component. With this restriction, here we obtain three new, different computational completeness results for some typical descriptional complexity measures. These results are crucially based on a variant of Special Geffert normal form (SGNF) of type-0 grammars, that we called space separating SGNF in a paper that appeared in Natural Computing in 2019.
Petri nets are a classical mathematical model used for several tasks, such as simulation of business processes, modelling of complex systems and so on. This model is based on a bipartite directed graph, where the set of places and the set of transitions mark the partition. There exists marks placed in each place in a specific way, whose representation depends on the problem being solved. A virus machine is a novel model of computation inspired by the spread and replication of viruses in real life, and has been used for applications such as cryptography and power systems fault diagnosis, among others. A virus machine can be represented by three well-differentiated graphs that mark the spaces where the viruses exist and move through, called hosts and channels, the control instructions, that direct the behaviour of the virus machine, and the instruction-channel graph that represents the control of the opening and closing of the channels. In this work, we use an extension of virus machines to simulate a specific variant of Petri nets, where there exist some restrictions. In fact, a direct protocol for the simulation is explicitly given.
The Turing Tumble is a mechanical puzzle game that simulates the operations of a computer processor using marbles and various mechanical components. The game allows for a visual representation of the computation and is widely used in the educational context. It was shown to be Turing-complete providing that an appropriate infinite configuration of the board, an infinite marble supply and the possibility to construct arbitrarily long frictionless gear chains are available. In this paper we show the computational universality of the game for a finite configuration and no unbounded gear chains. The only source of infinity is the supply of marbles and the unbounded drop capacity. We also provide a thoughtful analysis of the computation representation in Turing Tumble and discuss the possible input and output types.
Complexity of infinite words is a widely studied field in combinatorics on words. A classical notion of a complexity of an infinite word is defined as a function counting, for each n, the number of its distinct factors (or blocks of consecutive letters) of length n. In their 1938 seminal paper on symbolic dynamics, Morse and Hedlund gave a relation between factor complexity and periodicity in infinite words; namely, they proved that each aperiodic infinite word w has factor complexity at least n + 1 for each length n. They further showed that an infinite word.w has factor complexity n + 1 for each length n if and only if w is binary, aperiodic and balanced, i.e.,w is a Sturmian word. In this paper, we consider various modifications of the notion of a complexity of infinite words and generalizations of Morse and Hedlund theorem.
