Problem
Research questions and friction points this paper is trying to address.
simple semi-conditional grammars
non-terminals
complexity
RE languages
linear space
Non-Terminal Complexity of Simple Semi-Conditional Grammars
🤖 AI Summary
研究了简单半条件文法通过非终端数生成语言的能力及复杂性，确定了其上界和基本限制，并证明了二非终端文法的成员测试是NP难问题。
📝 Abstract
We study the complexity of simple semi-conditional grammars (SSCGs) in terms of the number of their terminals and non-terminals. We show that SSCGs with three non-terminals can generate all RE languages; two non-terminals suffice for linear languages; and one suffices for unary regular languages. We also determine both upper bounds and fundamental limitations of SSCGs: while certain one-non-terminal SSCGs can generate non-context-free languages, every language generated by a one-non-terminal SSCG is in non-deterministic linear space. We also prove that there exists a regular language of alphabet size at least 3 which cannot be generated by any one-non-terminal SSCG. Finally, we prove that membership testing for SSCGs of two non-terminals is already NP-hard.
Innovation
Methods, ideas, or system contributions that make the work stand out.
simple semi-conditional grammars
non-terminal complexity
RE languages
linear space
NP-hard
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