A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it is most useful for bottom-up deterministic wta, where it can be used for minimization and equivalence testing. In both applications a careful selection of the...

Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we analyze the convergence of the accuracy of reconstructing the root state in a complete binary tree of 2 as n goes to infinity and also give a lower bound on the accuracy of reconstructing the root state in an ultrametric ...

Reconstructing the phylogenetic relationships that unite all lineages (the tree of life) is a grand challenge. The paucity of homologous character data across disparately related lineages currently renders direct phylogenetic inference untenable. To reconstruct a comprehensive tree of life, we therefore synthesized published phylogenies, together with taxonomic classifications for taxa never in...

SUMMARY We have developed an efficient program, the Perfect Phylogeny Haplotyper (PPH) that takes in unphased population genotype data, and determines if that data can be explained by haplotype pairs that could have evolved on a perfect phylogeny.

We present an algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of characters is xed. This algorithm is simpler and faster than the known algorithms when the number of characters is at least 4.

Linguists use phylogenetic methods to build evolutionary trees of languages given lexical, phonological, and morphological data. Perfect phylogeny is too restrictive to explain most data sets. Conservative Dollo phylogeny is more permissive, and has been used in biological applications. We propose the use of conservative Dollo phylogeny as an alternative or complementary approach for linguistic...

The cophenetic metrics dφ,p, for p ∈ {0} ∪ [1,∞[, are a recent addition to thekit of available distances for the comparison of phylogenetic trees. Based on afifty years old idea of Sokal and Rohlf, these metrics compare phylogenetic treeson a same set of taxa by encoding them by means of their vectors of copheneticvalues of pairs of taxa and depths of single taxa, and then c...

In this paper we improve on an algorithm by Pachter-Speyer for reconstruction of a phylogenetic tree from its size-m subtree weights. We provide an especially efficient algorithm for reconstruction from 3-weights.