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This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.

6 votes
Accepted

Does IP = PSPACE work over other rings?

I think PSPACE does not make much sense over arbitrary rings (it is better to consider classes such as PAR). Consider $R=\mathbb Z$ or $R=\mathbb Q$ with order. You can encode any finite collection o …
Sergei Ivanov's user avatar
12 votes
Accepted

computational complexity

It is NP-complete. Here is a reduction from the graph 3-coloring problem. For a given graph, consider a sphere with $n$ holes where $n$ is the number of vertices. Enumerate the holes by the vertices …
Sergei Ivanov's user avatar