Knowledge compilation = query rewriting + view synthesis
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Combining Relational Algebra, SQL, and Constraint Programming
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Second-Order Logic over Strings: Regular and Non-regular Fragments
DLT '01 Revised Papers from the 5th International Conference on Developments in Language Theory
Predicate-calculus-based logics for modeling and solving search problems
ACM Transactions on Computational Logic (TOCL)
The model checking problem for prefix classes of second-order logic: a survey
Fields of logic and computation
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Fagin's (1974) theorem, the first important result of descriptive complexity, asserts that a property of graphs is in NP if and only if it is definable by an existential second-order formula. We study the complexity of evaluating existential second-order formulas that belong to prefix classes of existential second-order logic, where a prefix class is the collection of all existential second-order and the first-order quantifiers obey a certain quantifier pattern. We completely characterize the computation complexity of prefix classes of existential second-order logic in three different contexts: over directed graphs; over undirected graphs with self-loops; and over undirected graphs without self-loops. Our main result is that in each of these three contexts a dichotomy holds, i.e., each prefix class of existential second-order logic either contains sentences that can express NP-complete problems or each of its sentences expresses a polynomial-time solvable problem. Although the boundary of the dichotomy coincides for the first two cases, it changes, as one move to undirected graphs without self-loops.