Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Datalog extensions for database queries and updates
Journal of Computer and System Sciences
Feasible computation through model theory
Feasible computation through model theory
Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
Expressive Equivalence of Least and Inflationary Fixed-Point Logic
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
Elementary induction on abstract structures (Studies in logic and the foundations of mathematics)
ICCS'06 Proceedings of the 14th international conference on Conceptual Structures: inspiration and Application
The transfinite action of 1 tape turing machines
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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We consider an alternative semantics for partial fixed-point logic (PFP). To define the fixed point of a formula in this semantics, the sequence of stages induced by the formula is considered. As soon as this sequence becomes cyclic, the set of elements contained in every stage of the cycle is taken as the fixed point. It is shown that on finite structures, this fixed-point semantics and the standard semantics for PFP as considered in finite model theory are equivalent, although arguably the formalisation of properties might even become simpler and more intuitive. Contrary to the standard PFP semantics which is only defined on finite structures the new semantics generalises easily to infinite structures and transfinite inductions. In this generality we compare - in terms of expressive power - partial with other known fixed-point logics. The main result of the paper is that on arbitrary structures, PFP is strictly more expressive than inflationary fixed-point logic (IFP). A separation of these logics on finite structures would prove PTIME different from PSPACE.