## Fixpoint Logics, Relational Machines, and Computational Complexity (1993)

Venue: | In Structure and Complexity |

Citations: | 36 - 5 self |

### BibTeX

@INPROCEEDINGS{Abiteboul93fixpointlogics,,

author = {Serge Abiteboul and Moshe Y. Vardi and Victor Vianu},

title = {Fixpoint Logics, Relational Machines, and Computational Complexity},

booktitle = {In Structure and Complexity},

year = {1993},

pages = {156--168}

}

### Years of Citing Articles

### OpenURL

### Abstract

We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1st-order operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have the complexity classes between P and EXPTIME. Our parameterized fixpoint logics capture the complexity classes P, NP, PSPACE, and EXPTIME, but equality is achieved only over ordered structures. There is, however, an inherent mismatch between complexity and logic -- while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures. To overcome this mismatch, we develop a theory of relational complexity, which bridges tha gap between standard complexity and fixpoint logic. On one hand, we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complex...