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6 Declarative Workflow 183
executed between the first A and the subsequent B. The template precedence speci-
fies that task B can be executed only after task A is executed. Just like in the response
template, other tasks can be executed between tasks A and B. The combination of
the response and precedence templates defines a bi-directional execution order of
two tasks and is called succession. In this template, both response and precedence
relations have to hold between the tasks A and B. Template alternate precedence
strengthens the precedence template: tasks A and B have to alternate. The not coex-
istence template specifies that tasks A to B cannot both be executed in the same
instance. The 1of 4 template specifies that at least one of the three tasks A, B, C,
and D has to be executed, but all four tasks can be executed an arbitrary number of
times as long as one of them occurs at least once.

6.2.3 Branching of Templates

The behavior of models containing multiple constraints is given by the conjunction
of all constraints. In some cases it might be necessary to specify the disjunction
of constraints. This can be done by assigning more than two tasks to one parame-
ter in a template. When a template parameter is replaced by more than one task in
a constraint, then we say that this parameter branches. An example of a branched
precedence constraint is shown in Fig. 6.6, where parameter A has been replaced by
the task bill and parameter B is branched on tasks pickup and delivery. In case of
branching, the parameter is replaced (1) by multiple arcs to all branched tasks in
the graphical representation and (2) by a disjunction of branched tasks in the LTL
formula. The semantics of branching can vary from template to template, depending
on the LTL formula of the template. For example, the branched constraint in Fig. 6.6
specifies that each occurrence of bill must be preceded by at least one occurrence
of the task pickup or the task delivery. Note that it is possible to branch all parame-
ters, one parameter, or none of the parameters. The number of possible branches in
constraints is unlimited. For example, it is possible to branch the parameter B in the
response template to N alternatives, as shown in Fig. 6.6.
Another way of branching templates are choice templates, which can be used to
specify that one must choose between tasks. An example of such a template is the
1of 4 template (see Fig. 6.5), which is used to specify that at least one of the four
given tasks has to be executed.

6.2.4 An Example Language: ConDec

As explained before, we use LTL as a basis to define constraint templates. The
template is defined by specifying the corresponding LTL formula and graphical
representation. This makes it easy to create various languages, as any collection
of constraint templates forms a language. In this chapter, the focus is on the