Question 27336: One Split or Bounded Words Cannot Resolve the Pumping Quantifiers or Prove Regularity

Original question and givens

Use mode=bounded_words, complete model={"alphabet":["a","b"],"max_checked_length":1}. Give (mode, alphabet, max_checked_length, checked_word_count, regularity_proof_claim, boundary).

• G001 — Use mode=bounded_words, complete model={"alphabet":["a","b"],"max_checked_length":1}. Give (mode, alphabet, max_checked_length, checked_word_count, regularity_proof_claim, boundary).

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-pumping-lemma-regular-languages

Step-by-step derivation

source roles = [pump-boundary]

derived = [[mode, alphabet, max_checked_length, checked_word_count, regularity_proof_claim, boundary]]

source roles = [[a, b], 1]

derived = [[[0, 1, 1], [1, 2, 3]], 3, No]

Reverse checks

• S002 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.
• S001 · premise_and_result_audit — Reverse-check the complete original data,step operands and premises;finite checks,conditional named-theorem use and general formal proof remain distinct.

Result

(bounded_words, [a, b], 1, 3, No, bounded_words_do_not_prove_regular)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.