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We consider in this paper the problem of edge-minimization for nondeterministic finite automata and some connected questions. We shall formulate a new algorithm solving this problem; this algorithm is a simplification of two ones published before. The connected problems include at first algorithms of combining states. We formulate some new sufficient conditions for the possibility of such combining.

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In this paper, some heuristic decision-making techniques (methods) are considered that are used in various discrete optimization problems. The objective of each of these problems is the construction of anytime algorithms. The considered methods for solving these problems are constructed on the basis of a combination of some heuristics that belong to different areas of the theory of artificial intelligence.