A New Lower Bound Construction for the Word Problem for Commutative Thue Systems
A New Lower Bound Construction for the Word Problem for Commutative Thue Systems
Chee Keng Yap
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For 1 pass rule") (F2), Qfi^isbF, Al^Fi. Fc[inc]n[dec]Bt ("pass => dec rule") Let (5o, So) denote the Thue system corresponding to these rules. Remark: We write the rule (q, ^) as a — > /? above to be suggestive of the "forward" direction of applying the rules. But one must remember that we are describing a Thue system, so the reverse rule /? — ► or is also implied. A derivation that only uses the forward (resp. Reverse) rules will be called a /o ru;a nf (resp. Reverse) derivation; otherwise t...he derivation is mixed. Furthermore, if 07 — > ^7, we may write the rule as -r Q > 13 as in (SI) and (S2).
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