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Kuperberg, Denis
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 06/2021Conference Proceeding
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon's preservation theorem fails on finite structures. We additionally show that given a regular language, it is undecidable whether it is definable in FO+.
