Savitch's Theorem, proved by Walter Savitch in 1970, is a result of computational complexity theory stating that any problem a nondeterministic Turing machine can solve using f(n) space can also be solved by a deterministic Turing machine using space on the order of f(n) squared. It shows nondeterminism can inflate space usage by at most a quadratic factor, in sharp contrast to its apparently much larger effect on running time, and it implies that the complexity classes PSPACE and NPSPACE are equal, one of the few such class equalities known unconditionally.
Facts
StatementFor any space-constructible function f in Omega(log n), NSPACE(f(n)) is contained in DSPACE(f(n)^2). 2 Classification
Statement Form Sources
1. Savitch's theorem (Wikipedia)
Wikipedia Savitch's theorem lead paragraph (w-bbfill-psymath4-0926)Quote, Wikipedia Savitch's theorem lead paragraph (w-bbfill-psymath4-0926)
proved by Walter Savitch in 1970
2. Savitch's theorem, Wikipedia
Lead paragraphQuote, Lead paragraph
for any space-constructible function f ∈ Ω(log(n)), NSPACE(f(n)) ⊆ DSPACE(f(n)²).
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