By Thomas Zeume

"Small Dynamic Complexity sessions" used to be offered the E.W. Beth Dissertation Prize 2016 for amazing dissertations within the fields of common sense, language, and data. The thesis reviews the rules of question re-examination after enhancing a database. It explores the constitution of small dynamic descriptive complexity periods and offers new tools for proving reduce bounds during this dynamic context. one of many contributions to the previous element helped to verify the conjecture by way of Patnaik and Immerman (1997) that reachability might be maintained via first-order replace formulas.

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Here, we only looked at very basic graph query languages. Extensions, such as the query language ECRPQ [BLLW12], might be worth studying as well. As an example, the length of paths used in a conjunctive regular path query can be compared in ECRPQ. It is conceivable that such queries can be maintained in DynFO. This would also settle the open question whether a context-free path query can be maintained in DynFO when both insertions and deletions are allowed. As a minimal prerequisite for maintaining such queries, it is necessary to be able to maintain distances in a graph.

The new auxiliary relations are initialized accordingly. , [Pot03]). 44 3 Relating Small Dynamic Complexity Classes We note that, in this example, the application of the technique does not eliminate all quantifiers in the program (in fact, it removes one and introduces two new formulas with quantifiers), but it removes quantification from the update formula for a particular relation. 8. This concludes the description of the techniques. In the following, as a preparatory step, we generalize the preceding example and show how to remove quantifiers from the update formulas of the query relation for arbitrary DynFO-programs.

This is interesting for the same reason as studying the relationship of static classes. If two dynamic complexity classes DynC and DynC (induced by two static complexity classes C and C , respectively) — although they seem to be different at first glance — turn out to be equal, then queries that can be maintained in DynC can be maintained in DynC as well. In particular, when C is defined by syntactically restricting C, upper bounds for the more restricted class DynC can be obtained by showing upper bounds for the less restricted class DynC.

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