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Abstract: We prove that tree isomorphism is not expressible in the language (FO + TC + COUNT). This is surprising since in the presence of ordering the language captures NL, whereas tree isomorphism and canonization are in L ([L92]). Our proof uses an Ehrenfeucht-Fraiss'e game for transitive closure logic with counting [G91, IL90]. As a corresponding upper bound, we show that tree canonization is expressible in (FO + COUNT)[logn]. The best previous upper bound had been (FO + COUNT)[n O(1) ] ([DM90]).... (Update)
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.... that we will use to prove lower bounds on the number of boolean variables needed for the embeddings of PDL into FO 2 (TC) See [I98, EI95a, EW96] for discussions on Ehrenfeucht Frasse Games, and their extensions to transitive closure logic and temporal logic, respectively....
...to the number of variables as well as to the number of nested quantifiers in Q 1 . This strengthens a result of Etessami and Immerman [5] by which tree isomorphism is not definable in TC COUNTING. 1 Introduction We study two well known mechanisms of increasing the...
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BibTeX entry: (Update)
K. Etessami and N. Immerman, "Tree Canonization and Transitive Closure," IEEE Symp. Logic In Comput. Sci. (1995), 331-341. http://citeseer.ist.psu.edu/etessami95tree.html More
@article{ etessami00tree,
author = "Kousha Etessami and Neil Immerman",
title = "Tree Canonization and Transitive Closure",
journal = "Information and Computation",
volume = "157",
number = "1-2",
pages = "2-24",
year = "2000",
url = "citeseer.ist.psu.edu/etessami95tree.html" }
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1 The Ehrenfeucht-Fraisse Games for Transitive Closure (context) - Calo, Makowsky - 1992 ACM DBLP
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