arXiv subjects

Matthias Wendlandt

Publications and source records attributed to Matthias Wendlandt.

6 recordsLinked to original sources

arXiv2026

Inductive Inference of Cellular Automata

Inductive inference of one- and two-way cellular automata (CA) is considered. This involves inferring a CA that is compatible with a finite amount of available data. In this paper, this information is provided in the form of a finite set of intervals, where each interval consists of two words w and w' over a state set alphabet, with a positive integer i. The goal is to infer a CA which is compatible with each interval (w,w',i), meaning that it can derive w' from w in i steps. We consider three variations of this problem, 1) where the CA is completely known a priori, and the goal is therefore to verify compatibility, 2) where the CA is partially known a priori and the goal is to extend it to a full CA that is compatible, and 3) where the CA is completely unknown, and the goal is to fully construct one that is compatible if one exists. With all three variations, inference can be completed in polynomial time, and is in fact P-complete.

cs.FL↗

arXiv2026

Subregular Expressions and Their Expressive Power

We provide a survey of several families of subregular expressions obtained by modifying the classical operator set consisting of union, concatenation, and Kleene star. More specifically, we consider expression systems based on sets of two or three operations chosen from union, intersection, complementation, concatenation, and Kleene star. The resulting language families range from finite languages to the full class of regular languages. We collect and organize known results on the expressive power and structural properties of these families. We compare the resulting language classes over unary and arbitrary alphabets and summarize known inclusion, equality, and incomparability results. The aim of this survey is to provide a unified view of the language families induced by restricted operator sets and to highlight open relations and possible directions for further research.

cs.FL↗

arXiv2026

On some Open Problems for Finite Automata with Translucent Input Letters

Finite automata with translucent input letters are a recent model of discontinuous input processing. Basically, classical finite automata are equipped with a translucency function that defines, depending on the state, the set of translucent input symbols. While processing the input, translucent symbols are skipped and only visible symbols are read and processed. It is distinguished between deterministic and nondeterministic models and, in addition, between returning and non-returning models. In the former case, the automaton restarts from the left end of the input after having consumed some visible symbol, whereas in the latter case the automaton restarts from the left end of the input when the right endmarker symbol is seen. Returning finite automata with translucent letters have been introduced by Nagy and Otto and its non-returning variant has been introduced by Mraz and Otto. Many results concerning the computational capacity, relations between deterministic and nondeterministic models, and relations between returning and non-returning models are known. Moreover, some results on closure properties and decidability questions have been obtained as well. However, some questions have still been open since many years. In this paper, we will give answers to some of these open questions. In particular, we show the non-closure under concatenation, Kleene star, reversal, and inverse homomorphism for the non-returning deterministic as well as nondeterministic model. We also obtain non-closure under inverse homomorphism for the returning deterministic and nondeterministic model. Finally, we investigate the emptiness problem for non-returning finite automata with translucent input letters and show the decidability of the problem in case of deterministic as well as nondeterministic automata.

cs.FL↗

arXiv2025

Input-Driven Pushdown Automata with Translucent Input Letters

Input-driven pushdown automata with translucent input letters are investigated. Here, the use of translucent input letters means that the input is processed in several sweeps and that, depending on the current state of the automaton, some input symbols are visible and can be processed, whereas some other symbols are invisible, and may be processed in another sweep. Additionally, the returning mode as well as the non-returning mode are considered, where in the former mode a new sweep must start after processing a visible input symbol. Input-driven pushdown automata differ from traditional pushdown automata by the fact that the actions on the pushdown store (push, pop, nothing) are dictated by the input symbols. We obtain the result that the input-driven nondeterministic model is computationally stronger than the deterministic model both in the returning mode and in the non-returning mode, whereas it is known that the deterministic and the nondeterministic model are equivalent for input-driven pushdown automata without translucency. It also turns out that the non-returning model is computationally stronger than the returning model both in the deterministic and nondeterministic case. Furthermore, we investigate the closure properties of the language families introduced under the Boolean operations. We obtain a complete picture in the deterministic case, whereas in the nondeterministic case the language families are shown to be not closed under complementation. Finally, we look at decidability questions and obtain the non-semidecidability of the questions of universality, inclusion, equivalence, and regularity in the nondeterministic case.

cs.FL↗

arXiv2024

Complexity of Unary Exclusive Nondeterministic Finite Automata

Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with a special 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. We study the descriptional complexity of XNFA accepting unary languages. While the state costs for mutual simulations with DFA and NFA over general alphabets differ significantly from the known types of finite automata, it turns out that the state costs for the simulations in the unary case are in the order of magnitude of the general case. In particular, the state costs for the simulation of an XNFA by a DFA or an NFA are $e^{θ(\sqrt{n \cdot ln{n}})}$. Conversely, converting an NFA to an equivalent XNFA may cost $e^{θ(\sqrt{n \cdot ln{n}})}$ states as well. All bounds obtained are also tight in the order of magnitude. Finally, we investigate the computational complexity of different decision problems for unary XNFA and it is shown that the problems of emptiness, universality, inclusion, and equivalence are coNP-complete, whereas the general membership problem is NL-complete.

cs.FL↗

arXiv2017

Input-Driven Double-Head Pushdown Automata

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on acceptance if the heads meet. Demanding the automaton to work input-driven it is required that every input symbol uniquely defines the action on the pushdown store (push, pop, state change). Normally this is modeled by a partition of the input alphabet and is called a signature. Since our automaton model works with two heads either both heads respect the same signature or each head owes its own signature. This results in two variants of input-driven double-head pushdown automata. The induced language families on input-driven double-head pushdown automata are studied from the perspectives of their language describing capability, their closure properties, and decision problems.

cs.FL↗