# Tree Transducers

**Tree transducers**

## Introduction

Tree transducers are extensions of string transducers. Rather than locally mutating strings, tree transducers locally mutate parse trees.

Formal rules for intersection and composition of tree transducers make them amenable to phylogenetic alignment and in particular multiple RNA alignment.

Tree transducers can be used to perform structural alignment of multiple RNAs or even reconstruct possible ancestral RNA structures. Our programs, Evol Doer and Indie Gram, can (respectively) align & fold two non-coding RNAs (evoldoer) or reconstruct the most-probable ancestral structure of three non-coding RNAs (evolstar), using tree transducers to model RNA structural change.

### Alternate names

Tree transducers (or *parse tree transducers*) are essentially equivalent to Pair Stochastic Context-Free Grammars.

They are also closely related to pushdown automata.

"Pair HMMs on Tree Structures" (Sakakibara &: Pair hidden Markov models on tree structures. *Bioinformatics* 2003;19 Suppl 1:i232-40.) are similar models.

## References

- Bradley & Holmes: Evolutionary triplet models of structured RNA.
*PLoS Comput. Biol.*2009;5:e1000483.

- Computational linguistics
- Rounds, William C. 1970. Mappings and grammars on trees. Mathematical Systems Theory, 4(3):257–287.
- Thatcher, J. W. 1970. Generalized sequential machine maps. Journal of Computer and System Sciences, 4:339–367.
- Grael and Knight: http://www.isi.edu/natural-language/projects/rewrite/ttt.pdf
- TATA: http://tata.gforge.inria.fr/

- Bioinformatics
- Holmes &: A probabilistic model for the evolution of RNA structure.
*BMC Bioinformatics*2004;5:166. (PDF) - Sakakibara &: Pair hidden Markov models on tree structures.
*Bioinformatics*2003;19 Suppl 1:i232-40.

- Holmes &: A probabilistic model for the evolution of RNA structure.

## Software

The Evol Deeds package uses tree transducers:

- Evol Sayer does forward-simulation of a continuous-time model (the TKF structure tree) whose finite-time transitions can be described by a time-parameterized tree transducer
- Evol Doer does pairwise alignment & inference under this same model (TKF structure tree), using pair SCFGs
- Indie Gram, Robert Bradley's graduate project, creates a 4-tape SCFG via a three-transducer composition on a star toplogy, then uses this for multiple alignment & ancestral inference on 3 sequences