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State Complexity of Multiple Catenations

Caron P., Luque J.-G., Patrou B.

Fundamenta Informaticae

2018

Vol. 160, nr 3

255--279

We improve some results relative to the state complexity of the multiple catenations described by Gao and Yu. In particular we nearly divide by 2 the size of the alphabet needed for witnesses. We also give some refinements to the algebraic expression of the state complexity, which is especially complex with this operation. We obtain these results by using peculiar DFAs defined by Brzozowski.

Two-Dimensional Limited Context Restarting Automata

Krtek L., Mráz F.

Fundamenta Informaticae

2016

Vol. 148, nr 3/4

309--340

Motivated by possible machine learning of picture languages, we introduce a new twodimensional automaton called two-dimensional limited context restarting automaton. Our model is a simplification of the two-dimensional restarting tiling automaton, from which it differs in that it does not require to scan input pictures in a fixed order. We show that the two-dimensional limited context restarting automaton is equally powerful as the two-dimensional sgraffito automaton. Moreover, the correctness preserving version of the new model, while still being nondeterministic, is equivalent to the deterministic sgraffito automaton. However, the property of being correctness preserving is not even semi-decidable for two-dimensional limited context restarting automata.

Reversible Queue Automata

Kutrib M., Malcher A., Wendlandt M.

Fundamenta Informaticae

2016

Vol. 148, nr 3/4

341--368

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 automaton 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 ...[formula] 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.