Infinitary Logic and Inductive Definability over Finite Structures (1995)
| Venue: | Information and Computation |
| Citations: | 55 - 6 self |
BibTeX
@ARTICLE{Dawar95infinitarylogic,
author = {Anuj Dawar and Steven Lindell and Scott Weinstein},
title = {Infinitary Logic and Inductive Definability over Finite Structures},
journal = {Information and Computation},
year = {1995},
volume = {119},
pages = {160--175}
}
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Abstract
The extensions of first-order logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abiteboul and Vianu, 1991b] investigated the relationship of these two logics in the absence of an ordering, using a machine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, L ! 1! (see, for instance, [Kolaitis and Vardi, 1990]). We investigate this logic of finite structures and provide a normal form for it. We also present a treatment of the results in [Abiteboul and Vianu, 1991b] from this point of view. In particular, we show that we can write a formula of FO + LFP that defines ...
