Basic theory of feature trees

Abstract

We present a decision algorithm for the problem Val ( FT ) of deciding validity of first-order sentences in the theory of feature trees. Its time complexity is exp ⌊c·m⌋ ( c · n ) where n is the length of a sentence, m is the quantifier depth of a sequence, and c is a constant. The function exp i ( j ) is an exponential tower of 2's of height i , to power j (exp 0 ( j ) = j and exp i +1 ( j ) = 2 exp i ( j ) ). Moreover we prove that the presented algorithm is optimal, deriving a lower bound which matches the upper one.