IFIG Research Report
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Auflistung IFIG Research Report nach Autor:in "Jakobi, Sebastian"
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Item Grid graphs with diagonal edges and the complexity of Xmas mazes(2012) Holzer, Markus; Jakobi, SebastianWe investigate the computational complexity of some maze problems, namely the reachability problem for (undirected) grid graphs with diagonal edges, and the solvability of Xmas tree mazes. Simply speaking, in the latter game one has to move sticks of a certain length through a maze, ending in a particular game situation. It turns out that when the number of sticks is bounded by some constant, these problems are closely related to the grid graph problems with diagonals. If on the other hand an unbounded number of sticks is allowed, then the problem of solving such a maze becomes PSPACE-complete. Hardness is shown via a reduction from the nondeterministic constraint logic (NCL) of Demaine and Hearn to Xmas tree mazes.Item Minimal and hyper-minimal biautomata(2014) Holzer, Markus; Jakobi, SebastianWe compare deterministic finite automata (DFAs) and biautomata under the following two aspects: structural similarities between minimal and hyper-minimal automata, and computational complexity of the minimization and hyper-minimization problem. Concerning classical minimality, the known results such as isomorphism between minimal DFAs, and NL-completeness of the DFA minimization problem carry over to the biautomaton case. But surprisingly this is not the case for hyper-minimization: the similarity between almostequivalent hyper-minimal biautomata is not as strong as it is between almost-equivalent hyper-minimal DFAs. Moreover, while hyper-minimization is NL-complete for DFAs, we prove that this problem turns out to be computationally intractable, i.e., NP-complete, for biautomata.Item Minimization, characterizations, and nondeterminism for biautomata(2013) Holzer, Markus; Jakobi, SebastianWe show how to minimize biautomata with a Brzozowski-like algorithm by applying reversal and powerset construction twice. Biautomata were recently introduced in[O. Klíma, L. Polák: On biautomata. RAIRO Theor. Inf. Appl., 46(4), 2012] as a generalization of ordinary finite automata, reading the input from both sides. The correctness of the Brzozowski-like minimization algorithm needs a little bit more argumentation than for ordinary finite automata since for a biautomaton its dual or reverse automaton, built by reversing all transitions, does not necessarily accept the reversal of the original language. To this end we first generalize the notion of biautomata to deal with nondeterminism and moreover, to take structural properties of the forward- and backward-transition of the automaton into account. This results in a variety of biautomata models, which accepting power is characterized. As a byproduct we give a simple structural characterization of cyclic regular and commutative regular languages in terms of deterministic biautomata.Item A note on the computational complexity of some problems for self-verifying finite automata(2017) Holzer, Markus; Jakobi, SebastianWe consider the computational complexity of some problems for self-verifying finite automata (svFAs). In particular, we answer a question stated in the open problem session of the Workshop on Descriptional Complexity of Formal Systems 2015 held in Waterloo, Ontario, Canada, on the complexity of the promise version of the general membership problem for svFAs, showing that this problem is NL-complete.Item On the complexity of rolling block and Alice mazes(2012) Holzer, Markus; Jakobi, SebastianWe investigate the computational complexity of two maze problems, namely rolling block and Alice mazes. Simply speaking, in the former game one has to roll blocks through a maze, ending in a particular game situation, and in the latter one, one has to move tokens of variable speed through a maze following some prescribed directions. It turns out that when the number of blocks or the number of tokens is not restricted (unbounded), then the problem of solving such a maze becomes PSPACE-complete. Hardness is shown via a reduction from the nondeterministic constraint logic (NCL) of Demaine and Hearn to the problems in question. In this way we improve on a previous PSPACE-completeness result of Buchin and Buchin on rolling block mazes to best possible. Moreover, we also consider bounded variants of these maze games, i.e., when the number of blocks or tokens is bounded by a constant, and prove close relations to variants of graph reachability problems.Item On the computational complexity of partial word automata problems(2014) Holzer, Markus; Jakobi, Sebastian; Wendlandt, Matthias