Concurrency Theory: Lecture 7, 04 September 2019
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Trace language:

- Word language that is compatible with trace equivalence

- Regular trace language: trace language that is regular when
  viewed as set of strings

Trace prefix:

- For traces [w], [w'], [w] <= [w'] if [w'] "extends" [w].

  - For some u in [w] and u' in [w'], u is a prefix of u'

  - We call [w] a trace prefix of [w']

  - Example: With (a,b) in I, [b] <= [ab] because b in [b]
    and ba in [ab] such that b is a prefix of ba

- In the partial order representation, [w] <= [w'] if the partial
  order [w'] extends that of [w].  In other words [w] is
  downward closed subset of [w'].


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Constructing a canonical trace from a firing sequence:

- By induction build a net N_w = (P_w,T_w,F_w) and a marking M_w
  for each word w

- Let <=> denote trace equivalence. N_w is identical to N_w' for
  each w'<=> w: each concurrent run generates a canonical net

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