标题： Castor Ministerialis 显示英文标题

标题： Castor Ministerialis

摘要： 著名的忙碌海狸问题可以表述为：在开始于空白带的情况下，一个具有$n$个状态的图灵机（使用一个2符号字母表或者——在推广中——一个$m$符号字母表）能运行多久才能停止。因此，不停止的图灵机被排除在外。对于最多四个状态的情况，这个问题的答案是众所周知的。最近，已经验证了广泛认为的五状态候选者实际上是优胜者。并且，在寻找六状态或更多状态的好候选者方面取得了进展。我们研究了这个问题的一个变种：除了要求图灵机必须从空白带开始之外，我们只考虑那些在空白带上也会停止的图灵机。对于这个变种，我们给出了最多五状态的图灵机能运行多长时间的确定性答案，分析了一个六状态候选者的行为，并给出了一些关于具有$m$符号字母表的图灵机的一般化发现。 显示英文摘要

摘要： The famous problem of Busy Beavers can be stated as the question on how long a $n$-state Turing machine (using a 2-symbol alphabet or -- in a generalization -- a $m$-symbol alphabet) can run if it is started on the blank tape before it holds. Thus, not halting Turing machines are excluded. For up to four states the answer to this question is well-known. Recently, it could be verified that the widely assumed candidate for five states is in fact the champion. And there is progress in searching for good candidates with six or more states. We investigate a variant of this problem: Additionally to the requirement that the Turing machines have to start from the blank tape we only consider such Turing machines that hold on the blank tape, too. For this variant we give definitive answers on how long such a Turing machine with up to five states can run, analyze the behavior of a six-states candidate and give some findings on the generalization of Turing-machines with $m$-symbol alphabet.