What is the sequence of states that it will enter (including the start state)? Notice that you only need to evaluate half of the steps to determine the correct answer.

Question

BlackTom AI · Accepted Answer

We are given a multiple-choice question about the sequence of states a process will enter, including the start state, and a hint that only half of the steps need to be evaluated to determine the correct answer. Each option lists a full sequence of states from S0 up to S6, with various mid-sequence transitions.

Option 1: S0, S1, S2, S2, S2, S2, S3, S4, S4, S3, S3, S5, S3, S2, S2, S3, S3, S4, S4, S5, S5, S6
This option follows a pattern where after the initial S0 → S1 → S2 block, the transitions include a mix where S3 leads to S4 and then back to S3, which is plausible in some state diagrams but the specific sequence shows two consecutive S3 transitions after S4 that do not align with the expected half-step review indicated in the prompt. The repeated jump from S4 to S3 and then to S5 is inconsistent with the provided half-step evaluation hint and may indicate a misalignment in the state machine’s transitions.

Option 2: S0, S1, S2, S2, S2, S2, S3, S4, S4, S4, S4, S5, S5, S2, S2, S3, S3, S4, S4, S5, S5, S6
This path shows a clear and steady progression: after S0 → S1 → S2, the sequence advances to S3, then moves through a series of S4s, suggesting a holding or processing phase in S4, before transitioning to S5 and then a subsequent return to S2 before moving forward again to S3 and S4, and finally to S5 and S6. The distribution of transitions (especially the long run of S4 states and the return to S2) can be consistent with a halving or checkpoint-based evaluation where the key transitions are captured in the first half of steps, leading to the correct forward progression to S6.

Option 3: S0, S1, S3, S2, S2, S4, S2, S4, S4, S4, S4, S2, S5, S2, S2, S3, S3, S4, S4, S5, S5, S6
Here, the early deviation appears: after S0 and S1, this sequence jumps to S3 directly (S1 to S3) rather than S2, which indicates a divergent initial transition not typically expected from the standard path. The alternation between S2 and S4 later in the sequence also introduces transitions that may violate the half-step evaluation hint, making this option less consistent with the intended state progression.

Option 4: S0, S5, S3, S5, S2, S1, S4, S2, S3, S4, S4, S4, S3, S2, S1, S3, S3, S4, S4, S5, S5, S6
This option starts unusually with S0 followed by S5, which breaks the common expectation that the sequence begins with S1 immediately after S0. The later oscillations among S5, S3, and S2, and the multiple transitions back to S1 and S3 create a volatile pattern that seems inconsistent with a disciplined half-step evaluation approach. Overall, this path appears to deviate from the simplest, most progressive route toward S6.

In summary, each option presents a different trajectory through the state set {S0,...,S6}. Option 2 exhibits a steady, progressively forward-facing sequence with a plausible pattern of longer stays in intermediate states (notably S4) and a logical progression toward the final S6, aligning with the idea that half of the steps suffice to determine the correct overall path. The other options introduce early deviations, back-and-forth transitions, or unusual starting moves that conflict with the expected state-machine behavior suggested by the prompt.

COGSCI 200 001 WN 2025 Homework #3: Turing Machines and Decision Theory

What is the sequence of states that it will enter (including the start state)? Notice that you only need to evaluate half of the steps to determine the correct answer.

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