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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Emptiness problem | 1/1 | https://en.wikipedia.org/wiki/Emptiness_problem | reference | science, encyclopedia | 2026-05-05T11:33:06.962515+00:00 | kb-cron |
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
n
{\displaystyle n}
states, this is a decision problem that can be solved in
O
(
n
2
)
{\displaystyle O(n^{2})}
time, or in time
O
(
n
+
m
)
{\displaystyle O(n+m)}
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. 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.
== See also == Intersection non-emptiness problem
== References ==