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1
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1answer
107 views

Does hyper-computational power of infinite time Turing machines also require infinite memory?

Can a infinite time Turing machine perform hyper-computation like checking the consistency of the set theory ZF without using infinite memory?
2
votes
1answer
62 views

Satisfiability for various branching programs

Clearly, SAT for CNF, formula, or many classes of boolean circuits have strong significance on the entire theory community. Branching program, or BDD is one of the most basic and popular ...
8
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0answers
196 views

Linear space language that requires exponential time without ETH

The $\mathsf{P} \neq \mathsf{PSpace}$ conjecture means that There is a language $L \in \mathsf{DSpace}(O(n^t))$ for some $t>0$ such that for all positive integers $k$, $L$ requires ...
4
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0answers
93 views

Low space computation and branching program

One of the most elemental result of relationship between boolean circuit size and polynomial uniform computation is Pippenger and Fishers simulation: $DTIME[T(n)]\subseteq SIZE[T(n)\log T(n)]$. I ...
15
votes
3answers
939 views

How much time to recognize palindromes in logarithmic space?

It is well-known that palindromes can be recognized in linear time on $2$-tape Turing machines, but not on single-tape Turing machines (in which case the time needed is quadratic). The linear-time ...
2
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2answers
116 views

Nonregular Languages in Sublogarithmic Space

Are there any known languages that require $o(\log n)$ space but are also not regular? I'm looking for a problem "just below" undirected connectivity.
5
votes
1answer
156 views

Is the primality problem with unary input NLOGSPACE-Hard?

Consider the language $L=\{1^n : n \text{ is prime}\}$. Is this language NLOGSPACE-Hard? The motivation for this question is that $L$ is a good candidate for reducing to other languages related to my ...
4
votes
1answer
164 views

state-of-the-art bit complexity of the determinant

I'm trying to understand the full bit-complexity of computing the determinant of an $n\times n$ integer matrix, with each entry represented by $M$ bits. I would like to know what is the ...
12
votes
0answers
276 views

Non-deterministic logspace with two-sided error

The class BPL is the set of all problems solvable by a Turing machine running in logarithmic space and polynomial time with two-sided error; that is, if $x\in L$ then the machine accepts with ...
8
votes
1answer
178 views

Storing a bit vector in uninitialized memory and minimal space

A well-known trick for storing bit vectors using uninitialized memory can allocate a bit vector of size $n$ in which all of the bits are set to $0$ by allocating $(2 n + 1)\lceil \lg n \rceil$ bits of ...
14
votes
1answer
301 views

Space-approximation Trade-off

In their paper Approximate Distance Oracles, Thorup and Zwick showed that for any weighted undirected graph, it is possible to construct a data structure of size $O(k n^{1+1/k})$ that can return a ...
15
votes
2answers
479 views

What is the space complexity of calculating Eigenvalues?

I am looking for a survey paper or a book covering results about the space complexity of common linear algebra operations such as matrix rank, eigenvalues calculation, etc. I stress the "space ...
3
votes
1answer
736 views

Computational complexity of classifying with an already-trained SVM

If I have a support vector machine which has already been trained, what is the computational complexity of classifying a new example using that machine? I care about both time and space complexity. ...
8
votes
1answer
122 views

Savitch's use of measurability

In Savitch's 1969 paper, "Relationships Between Nondeterministic and Deterministic Tape Complexities", he states that "all common storage functions L(n) >= lg n are measurable. In particular, any ...
4
votes
0answers
482 views

Does L=P imply any new complexity class separations?

If L=P then P is not equal to PSPACE. This follows from PSPACE properly containing L. I am wondering if L=P implies any stronger separation between complexity classes? Does it imply P is properly ...
4
votes
2answers
142 views

Function with space-depending computation time

Does a function exist which is easily computable for one space capacity and is hard to compute for another? I am looking for a function which can be computed in polytime when available space is at ...
10
votes
1answer
484 views

Is Quasi-polynomial time in PSPACE?

I had done some search on this but I was not able to find an answer either way. Huck answered it fully. Thanks :)