Star-Freeness, First-Order Definability and Aperiodicity of Structured Context-Free Languages
Lecture Notes in Computer Science(2022)
摘要
A classic result in formal language theory is the equivalence among aperiodic finite automata, star-free regular expressions, and first-order logic on words. Extending these results to structured subclasses of context-free languages, such as tree languages, did not work as smoothly: there are star-free tree languages that are counting. We argue that investigating the same properties within the family of operator precedence languages (OPLs) by going back to string languages rather than tree languages may lead to equivalences that perfectly match those on regular languages. We define operator precedence expressions; we show that they define exactly the class of OPLs and that, when restricted to the star-free subclass, coincide with first-order definable OPLs and are aperiodic.
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关键词
Operator precedence languages,First-order logic,Monadic second-order logic,Star-free languages,Aperiodic languages,Input-driven languages,Visibly-pushdown languages
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