Editing Probabilistic context-free grammar (section)

====Design considerations====
PCFG design impacts the secondary structure prediction accuracy. Any useful structure prediction probabilistic model based on PCFG has to maintain simplicity without much compromise to prediction accuracy. Too complex a model of excellent performance on a single sequence may not scale.<ref name="Durbin 1998" /> A grammar based model should be able to:
* Find the optimal alignment between a sequence and the PCFG.
* Score the probability of the structures for the sequence and subsequences.
* Parameterize the model by training on sequences/structures.
* Find the optimal grammar parse tree (CYK algorithm).
* Check for ambiguous grammar (Conditional Inside algorithm).

The resulting of multiple [[parse tree]]s per grammar denotes grammar ambiguity. This may be useful in revealing all possible base-pair structures for a grammar. However an optimal structure is the one where there is one and only one correspondence between the parse tree and the secondary structure.

Two types of ambiguities can be distinguished. Parse tree ambiguity and structural ambiguity. Structural ambiguity does not affect thermodynamic approaches as the optimal structure selection is always on the basis of lowest free energy scores.<ref name="Dowell 2004" /> Parse tree ambiguity concerns the existence of multiple parse trees per sequence. Such an ambiguity can reveal all possible base-paired structures for the sequence by generating all possible parse trees then finding the optimal one.<ref name="Sipser 1996" /><ref name="Harrison 1978" /><ref name="Hopcroft 1979" /> In the case of structural ambiguity multiple parse trees describe the same secondary structure. This obscures the CYK algorithm decision on finding an optimal structure as the correspondence between the parse tree and the structure is not unique.<ref name="Giegerich 2000" /> Grammar ambiguity can be checked for by the conditional-inside algorithm.<ref name="Durbin 1998" /><ref name="Dowell 2004" />