59 lines
1.6 KiB
Markdown
59 lines
1.6 KiB
Markdown
---
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title: "Emptiness problem"
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chunk: 1/1
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source: "https://en.wikipedia.org/wiki/Emptiness_problem"
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category: "reference"
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tags: "science, encyclopedia"
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date_saved: "2026-05-05T11:33:06.962515+00:00"
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instance: "kb-cron"
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---
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In theoretical computer science and formal language theory, a formal language is empty if its set of valid sentences is the empty set. The emptiness problem is the question of determining whether a language is empty given some representation of it, such as a finite-state automaton. For an automaton having
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n
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{\displaystyle n}
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states, this is a decision problem that can be solved in
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O
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(
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n
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2
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)
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{\displaystyle O(n^{2})}
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time, or in time
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O
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(
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n
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+
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m
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)
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{\displaystyle O(n+m)}
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if the automaton has n states and m transitions. However, variants of that question, such as the emptiness problem for non-erasing stack automata, are PSPACE-complete. The emptiness problem in machine learning and formal languages determines if a model or automaton generates the empty language, which is undecidable for certain alternating multi-head finite automata over single-letter alphabets.
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The emptiness problem is undecidable for context-sensitive grammars, a fact that follows from the undecidability of the halting problem. It is, however, decidable for context-free grammars.
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== See also ==
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Intersection non-emptiness problem
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== References == |