Emptiness problem
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.[1] For an automaton having [math]\displaystyle{ n }[/math] states, this is a decision problem that can be solved in [math]\displaystyle{ O(n^2) }[/math] time,[2] or in time [math]\displaystyle{ O(n+m) }[/math] 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.[3] 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.[3]
See also
References
- ↑ Sipser, Michael (2012). Introduction to the Theory of Computation. Cengage Learning. ISBN 9781285401065.
- ↑ "Lecture 6: Properties of Regular Languages - II". Department of Computer Science, Columbia University. https://www.cs.columbia.edu/~aho/cs3261/Lectures/L6-Properties_of_Regular_Languages_II.html.
- ↑ 3.0 3.1 Hopcroft, J. E.; Ullman, J. D (1979). Introduction to Automata Theory, Languages, and Computation (first ed.). Addison-Wesley. ISBN 81-7808-347-7.
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