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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 the APX-hardness still holds even if one restricts the edge costs to an interval [1, 1 + ε], for an arbitrary… (More)

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)

The investigation of the possibility to eeciently compute approximations of hard optimization problems is one of the central and most fruitful areas of current algorithm and complexity theory. The aim of this paper is twofold. First, we introduce the notion of stability of approximation algorithms. This notion is shown to be of practical as well as of… (More)

An extended abstract of this paper has been presented at ICALP 2000. y Supported by DFG grant Hr-1413-2 and the project \Descriptional Complexity and EEcient Transformations of Formal Languages over Words, Trees, and Graphs" (common grant 864524 of DAAD and of the Academy of Finland). Abstract While deterministic nite automata seem to be well understood,… (More)