Deterministic space
In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine. It represents the total amount of memory space that a "normal" physical computer would need to solve a given computational problem with a given algorithm. It is one of the most well-studied complexity measures, because it corresponds so closely to an important real-world resource: the amount of physical computer memory needed to run a given program.
The measure DSPACE is used to define complexity classes, sets of all of the decision problems that can be solved using a certain amount of memory space. For each function f(n), there is a complexity class SPACE(f(n)), the set of decision problems that can be solved by a deterministic Turing machine using space O(f(n)). There is no restriction on the amount of computation time that can be used, though there may be restrictions on some other complexity measures (like alternation).
Several important complexity classes are defined in terms of DSPACE. These include:
Proof: Suppose that there exists a non-regular language L ∈ DSPACE(s(n)), for s(n) = o(log log n). Let M be a Turing machine deciding L in space s(n). By our assumption L ∉ DSPACE(O(1)); thus, for any arbitrary , there exists an input of M requiring more space than k.
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