It was recently shown that anti-unification over an equational theory consisting of only unit equations (more than one) is nullary. Such pure theories are artificial and are of little effect on practical aspects of anti-unification. In this work, we extend these nullarity results to the theory of semirings, a heavily studied theory with many practical applications. Furthermore, our argument holds over semirings with commutative multiplication and/or idempotent addition. We also cover a few open questions discussed in previous work.

中文翻译：

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反统一与半环理论

最近表明，仅由单位方程式（一个以​​上）组成的方程式理论的反统一是无效的。这种纯粹的理论是人为的，对反统一的实际影响不大。在这项工作中，我们将这些无效性结果扩展到半环理论上，该理论是经过广泛研究并具有许多实际应用的理论。此外，我们的论点保留了具有交换乘法和/或幂等加法的半环。我们还将涵盖先前工作中讨论的一些开放性问题。