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The invariant problem for binary string structures and the parallel complexity theory of queries. (English) Zbl 0766.68043
Summary: We define the isomorphism and canonical invariant problems as queries on finite structures, and show that they are first-order definable on binary string structures that include the bit predicate. Applying our results to the parallel complexity theory of queries, we prove a unique correspondence between complexity-derived query classes and parallel complexity classes closed under constant parallel time reducibility. This directly extends a similar theorem of A.Chandra and D. Harel [J. Comput. Syst. Sci. 25, 99-128 (1982; Zbl 0511.68073)] originally proved for sequential complexity classes closed under logarithmic space reducibility.

##### MSC:
 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) 68Q25 Analysis of algorithms and problem complexity 68P15 Database theory
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