Several types of systems of parallel communicating restarting automata are introduced andstudied. The main result shows that, for all types of restarting automata X, centralizedsystems of restarting automata of type X have the same computational power asnon-centralized systems of restarting automata of the same type and the same number ofcomponents. This result is proved by a direct simulation. In addition, it is shown thatfor one-way restarting automata without auxiliary symbols, systems of degree at least twoare more powerful than the component automata themselves. Finally, a lower and an upperbound are given for the expressive power of systems of parallel communicating restartingautomata.

Based on the formal framework of reaction systems by Ehrenfeucht and Rozenberg[Fund. Inform. 75 (2007) 263–280], reaction automata (RAs)have been introduced by Okubo et al. [Theoret. Comput. Sci.429 (2012) 247–257], as language acceptors with multiset rewritingmechanism. In this paper, we continue the investigation of RAs with a focus on the twomanners of rule application: maximally parallel and sequential. Considering restrictionson the workspace and the λ-input mode, we introduce the correspondingvariants of RAs and investigate their computation powers. In order to explore Turingmachines (TMs) that correspond to RAs, we also introduce a new variant of TMs withrestricted workspace, called s(n)-restricted TMs. Themain results include the following: (i) for a language L and a functions(n), L is accepted by ans(n)-bounded RA with λ-input mode insequential manner if and only if L is accepted by alog s(n)-bounded one-way TM; (ii) if a languageL is accepted by a linear-bounded RA in sequential manner, thenL is also accepted by a P automaton [Csuhaj−Varju and Vaszil, vol. 2597of Lect. Notes Comput. Sci. Springer (2003) 219–233.] in sequentialmanner; (iii) the class of languages accepted by linear-bounded RAs in maximally parallelmanner is incomparable to the class of languages accepted by RAs in sequential manner.

We introduce and investigate several variants of a bidirectional string assemblingsystem, which is a computational model that generates strings from copies of assemblyunits. The underlying mechanism is based on two-sided piecewise assembly of adouble-stranded sequence of symbols, where the upper and lower strand have to match. Thegenerative capacities and the relative power of the variants are our main interest. Inparticular, we prove that bidirectional string assembling system generate languages notrepresented as any finite concatenation of one-sided string assembling systems. The latterbuild an infinite, strict and tight concatenation hierarchy. Moreover, it is shown thateven the strongest system in question can only generate NL languages, while there areunary regular languages that cannot be derived. Furthermore, a finite strict hierarchywith respect to the different variants considered is shown and closure properties of thelanguages generated are presented.

In the literature various types of restarting automata have been studied that are basedon contextual rewriting. A word w is accepted by such an automaton if,starting from the initial configuration that corresponds to input w, theword w is reduced to the empty word by a finite number of applications ofthese contextual rewritings. This approach is reminiscent of the notion of McNaughtonfamilies of languages. Here we put the aforementioned types of restarting automata intothe context of McNaughton families of languages, relating the classes of languagesaccepted by these automata in particular to the class GCSL of growing context-sensitivelanguages and to the class CRL of Church–Rosser languages.

The recently introduced model of transducing by observing is compared with traditionalmodels for computing transductions on the one hand and the recently introduced restartingtransducers on the other hand. Most noteworthy, transducing observer systems withlength-reducing rules are almost equivalent to RRWW-transducers. With painter rules weobtain a larger class of relations that additionally includes nearly all rationalrelations.

Linear finite transducers underlie a series of schemes for Public Key Cryptography (PKC)proposed in the 90s of the last century. The uninspiring and arid language then used,condemned these works to oblivion. Although some of these schemes were afterwards shown tobe insecure, the promise of a new system of PKC relying on different complexityassumptions is still quite exciting. The algorithms there used depend heavily on theresults of invertibility of linear transducers. In this paper we introduce the notion ofpost-initial linear transducer, which is an extension of the notion of linear finitetransducer with memory, and for which the previous fundamental results on invertibilitystill hold. This extension enabled us to give a new method to obtain a left inverse of anyinvertible linear finite transducer with memory. It also plays an essencial role in thenecessary and sufficient condition that we give for left invertibility of linear finitetransducers.

We consider conditional tabled Lindenmayer sytems without interaction, where each table is associated with a regular set and a table can only be applied to a sentential form which is contained in its associated regular set. We study the effect to the generative power, if we use instead of arbitrary regular languages only finite, nilpotent, monoidal, combinational, definite, ordered, union-free, star-free, strictly locally testable, commutative regular, circular regular, and suffix-closed regular languages. Essentially, we prove that the hierarchy of language families obtained from conditional Lindenmayer systems with subregular conditions is almost identical to the hierarchy of families of subregular languages.