MIX is a 2-MCFL and the word problem in Z2 is captured by the IO and the OI hierarchies
Journal of Computer and System Sciences(2015)
摘要
In this work we establish that the language MIX={w∈{a;b;c}⁎||w|a=|w|b=|w|c} and the language O2={w∈{a;a¯;b;b¯}||w|a=|w|a¯∧|w|b=|w|b¯} are 2-MCFLs. As 2-MCFLs form a class of languages that is included in both the IO and OI hierarchies, and as O2 is the group language of a simple presentation of Z2 we exhibit here the first, to our knowledge, non-virtually-free group language (i.e. non-context-free group language) that is captured by the IO and OI hierarchies. Moreover, it was a long-standing open problem whether MIX was a mildly context sensitive language or not, and it was conjectured that it was not, so we close this conjecture by giving it a negative answer.
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关键词
Formal language theory,Mildly context sensitive languages,IO and OI hierarchies,Higher-order collapsible pushdown automata,Group languages,Algebraic topology,Jordan curves
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