Question 27331: One Split or Bounded Words Cannot Resolve the Pumping Quantifiers or Prove Regularity

Original question and givens

Use mode=wrong_quantifiers, complete model={"p":6,"word":["a","a","a","a","a","a","b"]}. Give (mode, p, word, legal_split_count, adversarial_choice_order, reversed_quantifier_claim).

• G001 — Use mode=wrong_quantifiers, complete model={"p":6,"word":["a","a","a","a","a","a","b"]}. Give (mode, p, word, legal_split_count, adversarial_choice_order, reversed_quantifier_claim).

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, p, word, legal_split_count, adversarial_choice_order, reversed_quantifier_claim]]

source roles = [wrong_quantifiers, 6, [a, a, a, a, a, a, b]]

derived = [21, adversary_word_then_prover_split_then_adversary_i, 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

(wrong_quantifiers, 6, [a, a, a, a, a, a, b], 21, adversary_word_then_prover_split_then_adversary_i, No)

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.