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• W2024823088 abstract "The article investigates the power of the dynamic complexity classes D yn FO, D yn QF, and D yn PROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in D yn PROP are exactly the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for D yn PROP and separates D yn PROP from D yn QF and D yn FO. Further, it is shown that any context-free language can be maintained in D yn FO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in D yn QF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: There exist first-order definable properties which are not maintainable in D yn PROP. On the other hand, any existential first-order property can be maintained in D yn QF when allowing precomputation." @default.
• W2024823088 created "2016-06-24" @default.
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• W2024823088 date "2012-08-01" @default.
• W2024823088 modified "2023-09-26" @default.
• W2024823088 title "The dynamic complexity of formal languages" @default.
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• W2024823088 doi "https://doi.org/10.1145/2287718.2287719" @default.
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