Descriptive characterizations of computational complexity
Journal of Computer and System Sciences
On the expressive power of database queries with intermediate types
Journal of Computer and System Sciences
Complete problems for fixed-point logics
Journal of Symbolic Logic
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Reduction to NP-complete problems by interpretations
Proceedings of the Symposium "Rekursive Kombinatorik" on Logic and Machines: Decision Problems and Complexity
Languages which capture complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Computing queries with higher-order logics
Theoretical Computer Science - Logic, language, information and computation
Extensions of MSO and the monadic counting hierarchy
Information and Computation
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Let i, j ≥1, and let Σ$^{i}_{j}$ denote the class of the higher order logic formulas of order i+1 with j–1 alternations of quantifier blocks of variables of order i+1, starting with an existential quantifier block. There is a precise correspondence between the non deterministic exponential time hierarchy and the different fragments of higher order logics Σ$^{i}_{j}$, namely NEXP$^{j}_{i}$ = Σ$^{i+1}_{j}$. In this article we present a complete problem for each level of the non deterministic exponential time hierarchy, with a very weak sort of reductions, namely quantifier-free first order reductions. Moreover, we don’t assume the existence of an order in the input structures in this reduction. From the logical point of view, our main result says that every fragment Σ$^{i}_{j}$ of higher order logics can be captured with a first order logic Lindström quantifier. Moreover, as our reductions are quantifier-free first order formulas, we get a normal form stating that each Σ$^{i}_{j}$ sentence is equivalent to a single occurrence of the quantifier and a tuple of quantifier-free first order formulas. Our complete problems are a generalization of the well known problem quantified Boolean formulas with bounded alternation (QBFj).