[英]the stack size in a PDA M can grow to hold at most k symbols. What kind of language is L(M)?
the stack size in a PDA M can grow to hold at most k symbols. PDA M 中的堆栈大小可以增长到最多容纳 k 个符号。 What kind of language is L(M)?
L(M) 是什么语言? Prove your claim.
证明你的主张。
I think the answer for this is this: The language L(M) is a regular language if it can hold at most k symbols.我认为答案是这样的:如果语言 L(M) 最多可以容纳 k 个符号,则它是一种常规语言。 Since it can hold at most k symbols, the stack size is therefore finite.
由于它最多可以容纳 k 个符号,因此堆栈大小是有限的。 Furthermore, we can create a DFA that will accept L(M), and therefore we can conclude that this language L(M) is regular.
此外,我们可以创建一个接受 L(M) 的 DFA,因此我们可以得出结论,该语言 L(M) 是正则的。
But I am having a debate with my friends whether this is correct or not但是我正在和我的朋友争论这是否正确
You are correct, such automata accept the regular languages.你是对的,这样的自动机接受常规语言。
One way to argue this is by showing how to construct an NFA for any of these limited-stack PDAs.论证这一点的一种方法是展示如何为这些有限堆栈 PDA 中的任何一个构建 NFA。 The construction is easy, as you have suggested and has been suggested in the comments:
构造很简单,正如您所建议的那样,并在评论中提出了建议:
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