arXiv subjects

Andreas Malcher

Publications and source records attributed to Andreas Malcher.

13 recordsLinked to original sources

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 $e^{\theta(\sqrt{n \cdot ln{n}})}$. Conversely, converting an NFA to an equivalent XNFA may cost $e^{\theta(\sqrt{n \cdot ln{n}})}$ 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↗

arXiv2023

Reversible Two-Party Computations

Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain on the one hand that there are regular languages that cannot be accepted by such systems. On the other hand, such systems can accept even non-semilinear languages. Since the systems communicate by sending messages, we consider also systems where the number of messages sent during a computation is restricted. We obtain a finite hierarchy with respect to the allowed amount of communication inside the reversible classes and separations to general, not necessarily reversible, classes. Finally, we study closure properties and decidability questions and obtain that the questions of emptiness, finiteness, inclusion, and equivalence are not semidecidable if a superlogarithmic amount of communication is allowed.

cs.FL↗

arXiv2022

Reversible Computations of One-Way Counter Automata

Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain separation results between irreversible and reversible k-counter automata for superpolynomial time. For exponential time we obtain moreover an infinite and tight hierarchy with respect to the number of counters. This hierarchy is shown with Kolmogorov complexity and incompressibility arguments. In this way, on passing we can prove this hierarchy also for ordinary counter automata. This improves the known hierarchy for ordinary counter automata in the sense that here we consider a weaker acceptance condition. Then, it turns out that k+1 reversible counters are not better than k ordinary counters and vice versa. Finally, almost all usually studied decidability questions turn out to be undecidable and not even semidecidable for reversible multi-counter automata, if at least two counters are provided.

cs.FL↗

arXiv2022

Computational and Descriptional Power of Nondeterministic Iterated Uniform Finite-State Transducers

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.

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↗

arXiv2014

Measuring Communication in Parallel Communicating Finite Automata

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of returning centralized systems, when the number of necessary communications during the computations of the system is bounded by a function depending on the length of the input. It is proved that an infinite hierarchy of language families exists, depending on the number of messages sent during their most economical recognitions. Moreover, several properties are shown to be not semi-decidable for the systems under consideration.

cs.FL↗

arXiv2012

Transductions Computed by One-Dimensional Cellular Automata

Cellular automata 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 allowed to process the input and to compute the output. Since there is a particular interest in fast transductions, we mainly focus on the time complexities real time and linear time. We first investigate the computational capabilities of cellular automaton transducers by comparing them to iterative array transducers, that is, we compare parallel input/output mode to sequential input/output mode of massively parallel machines. By direct simulations, it turns out that the parallel mode is not weaker than the sequential one. Moreover, with regard to certain time complexities cellular automaton transducers are even more powerful than iterative arrays. In the second part of the paper, the model in question is compared with the sequential devices single-valued finite state transducers and deterministic pushdown transducers. It turns out that both models can be simulated by cellular automaton transducers faster than by iterative array transducers.

cs.FL↗

arXiv2010

Remembering Chandra Kintala

With this contribution we would like to remember Chandra M. R. Kintala who passed away in November 2009. We will give short overviews of his CV and his contributions to the field of theoretical and applied computer science and, given the opportunity, will attempt to present the current state of limited nondeterminism and limited resources for machines. Finally, we will briefly touch on some research topics which hopefully will be addressed in the not so distant future.

cs.FL↗

arXiv2009

Bounded Languages Meet Cellular Automata with Sparse Communication

Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell communication by bounding the number of allowed uses of the links between cells. Moreover, we consider the devices as acceptors for bounded languages in order to explore the borderline at which non-trivial decidability problems of cellular automata classes become decidable. It is shown that even devices with drastically reduced communication, that is, each two neighboring cells may communicate only constantly often, accept bounded languages that are not semilinear. If the number of communications is at least logarithmic in the length of the input, several problems are undecidable. The same result is obtained for classes where the total number of communications during a computation is linearly bounded.

cs.FL↗

arXiv2009

Multi-Head Finite Automata: Characterizations, Concepts and Open Problems

Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple concept, their computational behavior can be already very complex and leads to undecidable or even non-semi-decidable problems on these devices such as, for example, emptiness, finiteness, universality, equivalence, etc. These strong negative results trigger the study of subclasses and alternative characterizations of multi-head finite automata for a better understanding of the nature of non-recursive trade-offs and, thus, the borderline between decidable and undecidable problems. In the present paper, we tour a fragment of this literature.

cs.CC↗

arXiv2009

Descriptional complexity of bounded context-free languages

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting arbitrary PDAs accepting ultralinear languages to finite-turn PDAs cannot be bounded by any recursive function. The latter phenomenon is known as non-recursive trade-off. In this paper, finite-turn PDAs accepting bounded languages are considered. First, letter-bounded languages are studied. We prove that in this case the non-recursive trade-off is reduced to a recursive trade-off, more precisely, to an exponential trade-off. A conversion algorithm is presented and the optimality of the construction is shown by proving tight lower bounds. Furthermore, the question of reducing the number of turns of a given finite-turn PDA is studied. Again, a conversion algorithm is provided which shows that in this case the trade-off is at most polynomial. Finally, the more general case of word-bounded languages is investigated. We show how the results obtained for letter-bounded languages can be extended to word-bounded languages.

cs.FL↗