Workflow audit trail
A fictional regulatory agency uses a five-state workflow for case files: Draft (D), Review (R), Approval (A), Published (P) and Archived (X). The permitted transitions are: D→R; R→A; R→D; A→P; A→R; P→X. A file may be returned from Review or Approval to an earlier stage at most twice in total. An internal audit checks three trails. Trail 1: D–R–A–R–A–P–X. Trail 2: D–R–D–R–A–P–X. Trail 3: D–R–A–P–R–A–P–X. The auditor must flag any trail that breaks the allowed transitions or the return limit, and must propose the smallest correction that makes the trail valid. A colleague argues that Trail 3 is acceptable because it eventually reaches Archived and because the file was only returned once. The audit is due in two working days.
1. Which trail(s) are invalid and why?
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Trail 3 is invalid. Its fourth transition is P→R: after a file is Published, the only permitted transition is P→X. Reaching Archived later does not cure an illegal intermediate step. Trail 1 is valid: D→R, R→A, A→R, R→A, A→P, P→X are all permitted; the single return A→R is within the limit. Trail 2 is also valid: D→R, R→D is one return, then D→R, R→A, A→P, P→X are permitted. The colleague is wrong to focus only on the final state and the return count; every adjacent transition must be allowed.
2. What is the smallest correction to Trail 3 that makes it valid under the stated rules?
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Delete the first P, the one immediately after the first A. Trail 3 becomes D–R–A–R–A–P–X, which is identical in form to Trail 1. Checking: D→R, R→A, A→R, R→A, A→P, P→X are all permitted, and there is one return (A→R), within the limit. This is a one-edit correction and is minimal because the invalid P→R transition must be removed or changed. Removing the later R–A–P segment would also work but requires three deletions, so it is not the smallest correction.
3. What does the colleague's argument overlook?
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It overlooks that workflow validity has two independent tests: every adjacent transition must be permitted, and the return limit must be respected. Trail 3 fails the first test at P→R; the later arrival at Archived and the number of returns cannot compensate for an illegal transition. The argument also mischaracterises the trail: the P→R step would be a return if it were allowed, but it is not allowed, so the trail fails at that point. The auditor should flag the illegal transition itself, not merely the final state or the return count.