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

Kutrib Martin, Malchers Andrea, Mereghetti Carlo, Palano Beatrice

Fundamenta Informaticae

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2022

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Vol. 185, nr 4

337--356

EN

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 NIUFSTs 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.

2

Two-Sided Strictly Locally Testable Languages

Holzer Markus, Kutrib Martin, Otto Friedrich

Fundamenta Informaticae

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2021

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Vol. 180, nr 1-2

29--51

EN

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two-sided strictly locally testable languages is shown to be a proper subclass of the even linear languages that is incomparable to the regular languages with respect to inclusion. Furthermore, closure properties of the class of two-sided strictly locally testable languages and decision problems are studied. Finally, it is shown that two-sided strictly k-testable languages are learnable in the limit from positive data.

3

Self-Verifying Pushdown and Queue Automata

Fernau Henning, Kutrib Martin, Wendlandt Matthias

Fundamenta Informaticae

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2021

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Vol. 180, nr 1-2

1--28

EN

We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and the answers given must not be contradictory. We show that SVPDA and SVRQA are automata characterizations of so-called complementation kernels, that is, context-free or realtime nondeterministic queue automaton languages whose complement is also context free or accepted by a realtime nondeterministic queue automaton. So, the families of languages accepted by SVPDA and SVRQA are strictly between the families of deterministic and nondeterministic languages. Closure properties and various decidability problems are considered. For example, it is shown that it is not semidecidable whether a given SVPDA or SVRQA can be made self-verifying. Moreover, we study descriptional complexity aspects of these machines. It turns out that the size trade-offs between nondeterministic and self-verifying as well as between self-verifying and deterministic automata are non-recursive. That is, one can choose an arbitrarily large recursive function f, but the gain in economy of description eventually exceeds f when changing from the former system to the latter.