A dominant cost for query evaluation in modern massively distributed systems is the number of communication rounds. For this reason, there is a growing interest in single-round multiway join algorithms where data is first reshuffled over many servers
and then evaluated in a parallel but communication-free way. The reshuffling itself is specified as a distribution policy. We introduce a correctness condition, called parallel-correctness, for the evaluation of queries w.r.t. a distribution policy. We study the complexity of parallel-correctness for conjunctive queries as well as transferability of parallel-correctness between queries. We also investigate the complexity of transferability for certain families of distribution policies, including, for instance, the Hypercube distribution.
This article shows that there exist two particular linear orders such that first-order logic with these two linear orders has the same expressive power as first-order logic with the Bit-predicate FO(Bit). As a corollary we obtain that there also exis
ts a built-in permutation such that first-order logic with a linear order and this permutation is as expressive as FO(Bit).
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXP
SPACE-completeness already holds for structures that do not include the induced successor relation. As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. A further consequence is that satisfiability of two-variable logic over data words with a linear order on positions and a linear order and successor relation on the data is decidable in EXPSPACE. As a complementing result, it is shown that over structures with two total preorder relations as well as over structures with one total preorder and two linear order relations, the finite satisfiability problem for two-variable logic is undecidable.
