The Workflow State Machine

A workflow description is called a workflow schema. It is a guarded automaton:

W = (S, T, E, C, A, V, s0)

with

• S is a set of states

• E is a set of events

• C is a set of conditions

• A is a set of actions

• V is a set of boolean variables

• Ass is a set of assignments: Ass subseteq V x {true, false}

• T is a set of transitions: T subseteq E x S --> S x CS x AS

  • with

  • CS subseteq C

  • AS = {(A1, ..., An)} for Ai in A union Ass and n in N0

• s0 in S is the initial state

A workflow instance is defined as follows:

I = (W, s, i)

with

• a workflow schema W = (S, T, E, C, A, V, s0)

• a current state s in S

• a variable instantiation i: V --> {true, false}

Be I = (W, s, i) a workflow instance. The successor of I for the event e is

(a) the workflow instance I' = (W, s', i') with

• there is a t in T with

  • t = (e, s, s', cs, as)

  • all c in cs are complied

• i'(v) = b for all v with (v, b) in as

• i'(v) = i(v) for all other v

(b) I, if such a t does not exist.

When an event e is invoked on a workflow instance I, the following algorithm is executed:

• The current state s_current is determined.
• The transition t from s_current to s_next which has the event e is determined.
• If t is not exactly defined, an exception is thrown.
• All conditions of t are validated.
• If all conditions are complied, the transition t fires:
  • All assignments of t are executed.
  • The workflow instance I is advanced to the state s_next.