A. Cal`o and J. Makowsky, "The Ehrenfeucht-Fraisse Games for Transitive Closure," 2nd Inter. Symp. on Logical Found. of Comp. Sci., (1992).

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Tree Canonization and Transitive Closure - Etessami, Immerman (1995)   (1 citation)  (Correct)

....formulas of non constant size. Recall that FO[t(n) denotes the set of properties expressible by firstorder formulas iterated t(n) times [I89a] 3 Ehrenfeucht Fraiss e Game for TC logic with Counting In this section we describe an E F game for the logic (FO TC COUNT) G91, IL90] see also [CM92] for a different E F game for TC) We will use it in section 4 to prove a lower bound on tree isomorphism. We first recall some notation for similar games such as the C k game from [IL90; CFI92] For a formula 2 (FO TC COUNT) let nd( denote the nesting depth, the combination of ....

A. Cal`o and J. Makowsky, "The Ehrenfeucht-Fraisse Games for Transitive Closure," 2nd Inter. Symp. on Logical Found. of Comp. Sci., (1992).

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