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On existentially first-order definable languages and their relation to NP

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (1998) 1443 LNCS 17-28
DOI: 10.1007/bfb0055037
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Abstract

Under the assumption that the Polynomial-Time Hierarchy does not collapse we show that a regular language L determines NP as an unbalanced polynomial-time leaf language if and only if L is existentially but not quantificifree definable in FO[

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Bordiert, B., Kuske, D., & Stephan, F. (1998). On existentially first-order definable languages and their relation to NP. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1443 LNCS, pp. 17–28). https://doi.org/10.1007/bfb0055037

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