## Computing With First-Order Logic (1995)

Citations: | 53 - 13 self |

### BibTeX

@MISC{Abiteboul95computingwith,

author = {Serge Abiteboul and Victor Vianu},

title = {Computing With First-Order Logic},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study two important extensions of first-order logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The fixpoint query computes an equivalence relation on tuples which is a congruence with respect to the rest of the computation. The same technique is used to show that equivalence of tuples and structures with respect to FO formulas with bounded number of variables is definable in fixpoint. Generalizing fixpoint and while, we consider more powerful languages which model arbitrary computation interacting with a database using a finite set of FO queries. Such computation is modeled by a relational machine...