3.1 Regular expression syntax notation

The description of a tree language with a finite depth limit suggests that CoGesT 1.1 can be formalised initially as a regular language, defined by a regular expression whose bracketing structure represents a tree structure with finite depth. For ease of semantic interpretation, the tree structure will then be represented by a context-free grammar in BNF notation, and this grammar will be translated directly into an XML DTD (cf. Table 1).

Table 1: Definition of CoGesT conventions as regular language (using abbreviations).

Complex Gesture CG:	$CG = GP (\hat{ } GP)^*$
Gesture Pair GP:	$GP = SG ( \epsilon \vert ( ; SG ) )$
Simplex Gesture SG:	$SG = So M$,
	$M = (\epsilon \vert D )$,
	$D = ( Tr \vert MG ( \hat{ } MG)^* ) Ta$
Microgesture MG:]	$MG = ( So Tr Ta )^*$

In Table 1 the following abbreviations are used: $M$, $D$, $So$, $Tr$, $Ta$ stand for Movement, Dynamic, Source, Trajectory, Target. The items Source, Trajectory, Target are variables over sequences of values. The regular expression for a Complex Gesture, down to the level of Simplex Gesture, is:

$CG = SG ( \epsilon \vert ( ; SG ) ) ( \hat{ } SG ( \epsilon \vert ( ; SG ) ) )^*$

The regular expression for a simplex gesture down to the level of microgesture is:

$SG = So (\epsilon \vert (Tr \vert MG ( \hat{ } MG)^* ) Ta )$

The overall regular expression down to the level of variables over vector values can be composed by replacing MG as defined above, and by replacing the other variables by disjunctions of their values or their value sequences, whichever is applicable (for further details, see the BNF notation below).