Problem
Research questions and friction points this paper is trying to address.
independent language property
language equation
regular operations
witness of non-satisfaction
Independent Languages and Witnesses of Dependence (Non-satisfaction)
🤖 AI Summary
研究通过语言方程φ(X)=∅解决独立语言问题，定义了非满足证人，并展示了如何计算正则语言的非满足证人，证明了该问题的决策版本是PSPACE完全的。
📝 Abstract
We consider the independent language property defined by the language equation Ï(X)=\emptyset, where the expression Ï involves the language variable X, constant languages, and standard regular operations including transductions, but not complementation. This property consists of all languages L satisfying Ï(L)=\emptyset. Depending on the choice of the operations in Ï, the equation defines a broad class of codes, including combinations of standard variable-length codes and error-detecting codes. We show that any Ï-independence is a Jürgensen independence, we define what a witness of non-satisfaction of Ï(X)=\emptyset is, for a language L, and we show how to compute a witness of non-satisfaction when L is regular. We also discuss the complexity of the problem, showing that the decision version of the problem is PSPACE-complete.
Innovation
Methods, ideas, or system contributions that make the work stand out.
independent language property
witness of non-satisfaction
regular languages
PSPACE-complete
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2024-02-20arXiv.orgCitations: 41
