• Source: 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. 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 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

Kata Kunci Pencarian:

• Filsafat Buddhis
• Aldo Capitini
• Emptiness problem
• Intersection non-emptiness problem
• Emptiness
• List of PSPACE-complete problems
• Empty set
• Alternating finite automaton
• Empty name
• Śūnyatā
• Maximum subarray problem
• NP-completeness