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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2018/digital-systems-linear-algebra-introduction-to-formal-proof/1/a/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Digital systems, linear algebra, introduction to formal proof / 1 / a / Solution by Codex 0 2026-10-31
Use a Moore machine whose state records the longest suffix of the received stream that is also a prefix of the target word. The transitions are
(1)
The last row preserves overlap: after recognition, one more one leaves suffix , giving . Initialize to and update the state on each active clock edge; the output after that edge reports whether the word has just ended. This is a prefix-suffix sequence recognizer.
Figure 1.
State transitions of the overlapping Moore machine recognizer
. Edge labels are input bits. Only the shaded, double-ring state produces output one. Details.
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