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 states, this is a decision problem that can be solved in time.[2] 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.

References

  1. ↑ Sipser, Michael (2012). Introduction to the Theory of Computation. Cengage Learning. ISBN 9781285401065.
  2. ↑ "Lecture 6: Properties of Regular Languages - II". COMS W3261 CS Theory. Department of Computer Science, Columbia University. Retrieved 2018-07-29.
  3. ↑ J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages, and Computation, first edition, 1979.
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