We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments from circuit complexity or algebra. Our proof is much more elementary, and uses only the most basic facts about finite automata.

翻译：我们给出了一个简单的新证据,证明由第一级判决定义的正常语言,没有限定更改,可以用只出现正常原子公式的句子来定义。 早期的事实证据依赖于电路复杂度或代数的论据。 我们的证据更基本得多,只使用有限的自动数据的最基本事实。