This paper presents a decidable characterization of tree languages??that can be defined by a boolean combination of $\Sigma_1$??formulas. This is a tree extension of the Simon theorem, which says??that a string language can be defined by a boolean combination of??$\Sigma_1$ formulas if and only if its syntactic monoid is??$J$-trivial.
Index Terms:
logic, algebra, tree automata
Citation:
Mikolaj Bojanczyk, Luc Segoufin, Howard Straubing, "Piecewise Testable Tree Languages," lics, pp.442-451, 2008 23rd Annual IEEE Symposium on Logic in Computer Science, 2008