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Abstract: We show that transitive closure logic (FO + TC) is strictly more powerful than deterministic transitive closure logic (FO + DTC) on finite (unordered) structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every DTC-query is bounded and therefore first order expressible. On the other hand there are simple (FO + pos TC) queries on these classes that cannot be defined by first order formulae. (Update)
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.... Most important complexity classes below P have had their languages without ordering, or with some partial orderings, separated [10, 11, 9, 5, 4]. No such separation had been proved for the languages (FO(wo) LFP) and (FO(wo) PFP) In 1991 Abiteboul and Vianu explained why by...
.... Most important complexity classes below P have had their languages without ordering, or with some partial orderings, separated [13, 14, 9, 6, 5]. No such separation had been proved for the languages FO(wo) LFP) and FO(wo) PFP) In 1991 Abiteboul and Vianu explained why by...
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BibTeX entry: (Update)
E. Gradel and G. McColm, "On the Power of Deterministic Transitive Closures," Information and Computation (119:1) (1995), 129-135. http://citeseer.ist.psu.edu/388257.html More
@article{ gradel95power,
author = "E. Gr{\a}del and G. {McColm}",
title = "the Power of Deterministic Transitive Closures",
journal = "Information and Computation",
volume = "119",
number = "1",
pages = "129--135",
year = "1995",
url = "citeseer.ist.psu.edu/388257.html" }
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