Sebastian Seibert

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It is proved that every regular expression of size n can be converted into an equivalent nondeterministic nite automaton (NFA) of size O(n(log n) 2) in polynomial time. The best previous conversions result in NFAs of worst case size (n 2). Moreover, the nonexistence of any linear conversion is proved: we give a language Ln described by a regular expression(More)
While deterministic finite automata seem to be well understood, surprisingly many important problems concerning nondeterministic finite automata (nfa’s) remain open. One such problem area is the study of different measures of nondeterminism in finite automata and the estimation of the sizes of minimal nondeterministic finite automata. In this paper the(More)
In this paper we investigate the problem of finding a 2-connected spanning subgraph of minimal cost in a complete and weighted graph G. This problem is known to be APX-hard, for both the edge and the vertex connectivity case. Here we prove that theAPX-hardness still holds even if one restricts the edge costs to an interval [1, 1+ε], for an arbitrary small ε(More)
While deterministic nite automata seem to be well understood, surprisingly many important problems concerning nondeterministic nite automata (nfa's) remain open. One such problem area is the study of di erent measures of nondeterminism in nite automata and the estimation of the sizes of minimal nondeterministic nite automata. In this paper the concept of(More)
Three types of finite-state graph automata are compared over directed acyclic graphs (where vertices and edges are labelled). The automata are distinguished by the way how states are attached to an input graph (“vertexmarking”, “edge-marking”, and “1-sphere-marking”). We note the equivalence of these models, relate them to logical definability notions, and(More)