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Complexity classes for BSS machines

Given a first-order structure $\mathcal{S}$, a Blum-Shub-Smale machine on $\mathcal{S}$ is essentially a Turing machine where Cells on the tape can hold arbitrary elements of $\mathcal{S}$. The ...
Noah Schweber's user avatar
5 votes
0 answers
192 views

Complexity implications on computability

Are there any known links between complexity theory and computability theory by which I mean non-trivial theorems of the form: If NP $\neq$ co-NP then there is no strong minimal pair of r.e. sets or ...
Peter Gerdes's user avatar
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5 votes
0 answers
246 views

Does $\mathsf{Q}$ have any interesting provably recursive functions?

This question was asked and bountied at MSE without success. For an appropriate theory $T$, say that an $n$-ary $T$-provably recursive function is a $\Sigma_1$ formula $\varphi$ with $n+1$ free ...
Noah Schweber's user avatar
5 votes
0 answers
106 views

Collapsing the Exponential time Hierarchy with a complete language as oracle

It is known that $\mathsf{P^A=NP^A}$ is true for every $\mathsf{EXP}$ complete language $\mathsf{A}$. The question is the whether the similar things hold for Exponential time Hierarchy. Is there ...
Erfan Khaniki's user avatar
4 votes
0 answers
214 views

Computational complexity of zeros of an analytic function

The work of Friedman and Ko, page 342, Corollary 4.3.1 states that all zeros of analytic polynomial time computable function are polynomial time computable, but for me that is not clear how it could ...
poeaqnwgo's user avatar
4 votes
0 answers
568 views

About "natural proof" of Razborov and Rudich

The famous "Natural Proof" paper ,http://www.cs.umd.edu/~gasarch/BLOGPAPERS/natural.pdf , ‎of Razborov and Rudich gives a barrier for any proof that try to separate P and NP. It mainly shows that if ...
Hao Yu's user avatar
  • 781
3 votes
0 answers
146 views

Lower Bound of Solutions to P=NP?

Do we at least know that simulating polynomial time non-deterministic Turing machines requires more than a linear slowdown? That is, do we know there is some non-deterministic Turing machine with ...
Peter Gerdes's user avatar
  • 3,029
3 votes
0 answers
186 views

Decidable equality for computable functions $\mathbb{N}\to\mathbb{N}$

Suppose we have two computable functions $f, g:\mathbb{N}\to\mathbb{N}$. When is $f=g$ algorithmically decidable? For example it is decidable if $f$ and $g$ are polynomials of a priori known degree.
Laika's user avatar
  • 31
2 votes
0 answers
90 views

Recursion theoretical Characterization of time complexity classes

Is there any known Recursion theoretical Characterization of time complexity classes like $\mathsf{DTIME(n^k)}$ or $\mathsf{NTIME(n^k)}$ for some fixed $k$? Thanks.
Erfan Khaniki's user avatar
2 votes
0 answers
163 views

Graph theoretical representation of Wang Tile

We note that for one dimensional tiling problem of Wang Tile could be represented by a graph. Each cycle on the graph represents a periodic solution. However, is there a well established counter-part ...
user40780's user avatar
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