The use of translucent input letters represents a way of implementing a discontinuous input processing in automata. In detail, a translucent automaton performs several sweeps from left to right on the input: according to the current state, some symbols are visible and can be processed, whereas some other symbols are invisible and may be processed in another sweep. We also distinguish between the returning and non-returning mode, which differ in the way the automaton behaves after reading a symbol: in the returning mode, a new sweep starts immediately, while in the non-returning mode, the device processes the next visible symbol. Here, we investigate deterministic pushdown automata with translucent letters both in the returning and non-returning mode. We prove that the non-returning mode strictly outperforms the returning mode, and that the families of the languages accepted by these two types of devices can be ranked strictly between the deterministic context-free languages and the deterministic context-sensitive languages. Moreover, both families are shown to be incomparable to the families of context-free, growing context-sensitive, and Church-Rosser languages. The ability of accepting non-semilinear languages is also emphasized (addressing an open question in the literature). Finally, we study the closure properties of both language families under the Boolean operations, obtaining that they are both closed under complementation but not under union and intersection. Further non-closure results are pointed-out for returning devices.

Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with an exclusive-or-like acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than one accepting paths, the input is rejected. It turns out that, from a descriptional complexity point of view, XNFAs differ significantly from the known types of finite automata. In particular the state costs for the simulation of an XNFA by a DFA are states, while the costs for simulating an XNFA by an NFA are states. Both bounds are also shown to be tight. On the other hand, NFAs may have advantages in comparison to XNFAs. For the simulation of an NFA by an XNFA, a tight bound of states is given. Finally, we investigate the computational complexity of different decision problems for XNFAs and it turns out that emptiness, universality, inclusion, and equivalence are PSPACE -complete.

Input-driven pushdown automata (IDPDAs) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that every push operation pushes exactly one additional symbol on the pushdown store and, in addition, stationary moves are not allowed so that the devices work in real time. Here, we relax this strong definition and consider IDPDAs that may push more than one symbol in one step (push-IDPDA) or may perform stationary moves (stat-IDPDA). We study the computational power of the extended variants both in the deterministic and nondeterministic case, we investigate several decidability questions for the new automata classes, and we obtain interesting representations by inverse homomorphisms. Namely, every (1) deterministic, (2) real-time deterministic, and (3) nondeterministic context-free language can be characterized as the inverse homomorphic image of a language accepted by a (1) stat-IDPDA, (2) push-IDPDA, and (3) nondeterministic push-IDPDA.

An iterated uniform finite-state transducer executes the same length-preserving transduction in iterative sweeps. The first sweep occurs on the input string, while any subsequent sweep works on the output of the previous one. All sweeps always start from the sole initial state. The device accepts upon halting in an accepting state at the end of a sweep. We consider devices with one-way sweep motion and two-way sweep motion, i.e., sweeps are either from left to right only, or strictly alternate from left to right and from right to left. In addition, devices may work deterministically or nondeterministically. We focus on iterated uniform finite-state transducers accepting unary languages, i.e., languages built over single-letter alphabets. We show that any unary regular language can be accepted by a deterministic iterated uniform finite-state transducer with at most max⁡{2⋅ϱ,p}+1 states, where ϱ and p are the greatest primes in the factorization of the, respectively, pre-periodic and periodic part of the language. Such a state cost cannot be improved by using two-way motion, and it turns out to greatly outperform in the worst case the state costs of equivalent classical models of finite-state automata. Next, we give a characterization of classes of unary languages accepted by non-constant sweep-bounded iterated uniform finite-state transducers in terms of time-bounded one-way cellular automata. This characterization enables both to exhibit interesting families of unary nonregular languages accepted by iterated uniform finite-state transducers, and to prove the undecidability of several questions related to iterated uniform finite-state transducers accepting unary languages with an amount of sweeps that is at least logarithmic.

Abstract We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreversible. In detail, we study the operational descriptional complexity of deterministic and nondeterministic undirected finite automata. To this end, the different types of automata on alphabets with few letters are characterized. Then, the operational state complexity of the Boolean operations as well as the operations concatenation and iteration is investigated, where tight upper and lower bounds are derived for unary as well as arbitrary alphabets under the condition that the corresponding language classes are closed under the operation considered.

An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST) version of this device. We show that constant sweep bounded IUFSTs and NIUFSTs accept all and only regular languages. We study the state complexity of removing nondeterminism as well as sweeps on constant sweep bounded NIUFSTs, the descriptional power of constant sweep bounded IUFSTs and NIUFSTs with respect to classical models of finite-state automata, and the computational complexity of several decidability questions. Then, we focus on non-constant sweep bounded devices, proving the existence of a proper infinite nonregular language hierarchy depending on the sweep complexity both in the deterministic and nondeterministic case. Though NIUFSTss are "one-way" devices we show that they characterize the class of context-sensitive languages, that is, the complexity class DSpace(lin). Finally, we show that the nondeterministic devices are more powerful than their deterministic variant for a sublinear number of sweeps that is at least logarithmic.

Abstract Iterative arrays whose internal inter-cell communication is quantitatively restricted are investigated. The quantity of communication is measured by counting the number of uses of the links between cells. In particular, iterative arrays are studied where the maximum number of communications per cell occurring in accepting computations is drastically bounded by a constant number. Additionally, the iterative arrays have to work in realtime. We study the computational capacity of such devices. For example, a result is that a strict and dense hierarchy with respect to the constant number of communications exists. Due to their very restricted communication, the question arises whether the usually studied decidability problems such as, for example, emptiness, finiteness, inclusion, or equivalence become decidable for such devices. However, it can be shown that all such decidability questions remain undecidable even if only four communications per cell are allowed. Finally, the undecidability results are shown to hold as well for one-way and two-way cellular automata having at most four communications per cell.

Abstract To determine the computational capacity of cellular automata they are often investigated towards their ability to accept formal languages within certain time constraints. In this paper, we take up an opposite position and look at cellular automata towards their ability to generate patterns, within certain time constraints. As an example we describe a construction of a cellular automaton that generates prefixes of the Oldenburger–Kolakoski sequence within real time. Furthermore, we study the real-time generation of unary and non-unary patterns in depth. In the unary case, we obtain a characterization by time-constructible functions and their corresponding unary formal languages. In the non-unary case, we provide constructions that generate any arbitrary given properly thin context-free language as well as all prefixes of any given automatic sequence.

Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes are incomparable with the regular languages. On the other hand, it is possible to generate non-semilinear languages with systems having contexts of length two. Here, we study decidability questions for insertion systems. On the one hand, it can be seen that emptiness and universality are decidable. Moreover, the fixed membership problem is solvable in deterministic polynomial time. On the other hand, the usually studied decidability questions such as, for example, finiteness, inclusion, equivalence, regularity, inclusion in a regular language, and inclusion of a regular language turn out to be undecidable. Interestingly, the latter undecidability results can be carried over to other models which are basically able to handle the mechanism of inserting strings depending on contexts. In particular, new undecidability results are obtained for pure grammars, restarting automata, clearing restarting automata, and forgetting automata.

In input-driven automata the input alphabet is divided into distinct classes and different actions on the storage medium are solely governed by the input symbols. For example, in input-driven pushdown automata (IDPDA) there are three distinct classes of input symbols determining the action of pushi ng, popping, or doing nothing on the pushdown store. Here, input-driven automata are extended in such a way that the input is preprocessed by a deterministic sequential transducer. IDPDAs extended in this way are called tinput-driven pushdown automata (TDPDA) and it turns out that TDPDAs are more powerful than IDPDAs but still not as powerful as real-time deterministic pushdown automata. Nevertheless, even this stronger model has still good closure and decidability properties. In detail, it is shown that TDPDAs are closed under the Boolean operations union, intersection, and complementation. Furthermore, decidability procedures for the inclusion problem as well as for the questions of whether a given automaton is a TDPDA or an IDPDA are developed. Additionally, representation theorems for the context-free languages using IDPDAs and TDPDAs are established. Two other classes investigated are on the one hand TDPDAs restricted to tinput-driven counter automata and on the other hand TDPDAs generalized to tinput-driven stack automata. In both cases, it is possible to preserve the good closure and decidability properties of TDPDAs, namely, the closure under the Boolean operations as well as the decidability of the inclusion problem.

Deterministic finite automata equipped with the storage medium of a queue are investigated towards their ability to perform reversible computations, that is, computations in which every occurring configuration has exactly one successor and exactly one predecessor. A first result is that any queue a utomaton can be simulated by a reversible one. So, reversible queue automata are as powerful as Turing machines. Therefore it is of natural interest to impose time restrictions to queue automata. Here we consider quasi realtime and realtime computations. It is shown that every reversible quasi realtime queue automaton can be sped up to realtime. On the other hand, under realtime conditions reversible queue automata are less powerful than general queue automata. Furthermore, we exhibit a lower bound of Ω(n2log(n)) time steps for realtime queue automata witness languages to be accepted by any equivalent reversible queue automaton. We study the closure properties of reversible realtime queue automata and obtain similar results as for reversible deterministic pushdown automata. Finally, we investigate decidability questions and obtain that all commonly studied questions such as emptiness, finiteness, or equivalence are not semidecidable for reversible realtime queue automata. Furthermore, it is not semidecidable whether an arbitrary given realtime queue automaton is reversible.

The parallel models of cellular automata and iterative arrays are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time al