Relating refined space complexity classes

Implicit Computational Complexity and the Exponential Time-Space Classes

We extend the Implicit Computational Complexity program, promoted by Leivant and by other scholars, to all complexity classes DTIMESPACEF(f(n), g(n)), between DTIMEF(n) and DSPACEF(nn c ). Let clps(α, n) denote the result of replacing ω by n in Cantor normal form for α < ωω ω . A hierarchy T Sαβ is defined by means of a very restricted form of substitution, and of two un-limited operators (simu...

A Sharp Separation of Sublogarithmic Space Complexity Classes

We present very sharp separation results for Turing machine sublogarithmic space complexity classes which are of the form: For any, arbitrarily slow growing, recursive nondecreasing and unbounded function s there is a k ∈ N and an unary language L such that L ∈ SPACE(s(n) + k) \ SPACE(s(n − 1)). For a binary L the supposition lim s = ∞ is sufficient. The witness languages differ from each langu...

Notes for Lecture 7 1 Space - Bounded Complexity Classes

A machine solves a problem using space s(·) if, for every input x, the machine outputs the correct answer and uses only the first s(|x|) cells of the tape. For a standard Turing machine, we can’t do better than linear space since x itself must be on the tape. So we will often consider a machine with multiple tapes: a read-only “input” tape, a read/write “work” or “memory” tape, and possibly a w...

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes

Reversible computing can reduce the energy dissipation of computation, which can improve cost-efficiency in some contexts. But the practical applicability of this method depends sensitively on the space and time overhead required by reversible algorithms. Time and space complexity classes for reversible machines match conventional ones, but we conjecture that the joint space-time complexity cla...

Relativized Separation of Reversible and Irreversible Space-Time Complexity Classes