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Related are problems that admit algorithms with polynomial delay. The first solution, and every solution thereafter, can be generated in polynomial time. Johnson, Yannakakis, and Papdimitriou discus …

Expanding on Anand Kulkarni's comment: Suppose there is a deterministic Turing machine M that recognizes SAT in polynomial time. Then the finite transition relation of M will be a function. We know …

Problems requiring a solution can be turned into decision problems if there is some way to measure how good a solution is. The decision version specifies that any solution must be better than some th …

I am not sure I would go along with your characterization that adding a single edge to the input makes the problem NP-complete, since one is actually allowing an edge to be added to every one of the i …

INDEPENDENT SET is NP-complete for (cross,triangle)-free graphs, but can be solved in linear time for (chair,triangle)-free graphs. (The X-free graphs are those that contain no graph from X as an ind …

Several graph products can be recognized in polynomial time. As usual the Cartesian product is the easiest, and the Cartesian case is also the basis for the algorithms for several other products. Re …

Barrington, Immerman, and Straubing state circuit complexity classes contain problems which are not computable at all in the ordinary sense (e.g., any unary language is in $\text{AC}^0$) I'd app …

For attempts to separate the bounded nondeterminism hierarchy, I think monotone dualization of prime formulas is the most salient topic. Consider the decision problem MONOTONE DUAL Input: two m …

As far as I can tell, UniqueSAT is exponentially dense, in the sense that it contains $2^{\Omega(n)}$ instances of size $n$. (This is a stronger requirement than $2^{n^\varepsilon}$ for infinitely man …

Let $X_m=[m]=\{0,1,\dots,m-1\}$ and let $Y_m=[2m]\setminus [m]$. Given is a complete bipartite graph $G_m$, with parts $X_m$ and $Y_m$ and edges $\{x,y\}$ for every $x\in X_m$ and $y\in Y_m$. Alice an …

Is it true that $$O(n) = \bigcap \{ O(g) \mid g \in \omega(n) \}?$$ This appears to be a straighforward question about sets of functions, but on closer examination leads to some murky waters. I woul …

Tsuyoshi Ito's elegantly sparse phrasing in another answer does not explicitly say so, but perhaps it is worth pointing out: any sparse language is in P/poly. Then also any tally language is in P/pol …

In The computational complexity of linear optics (ECCC TR10-170), Scott Aaronson and Alex Arkhipov argue that if quantum computers can be efficiently simulated by classical computers then the polynomi …

The Complexity Zoo points out in the entry on EXP that if L = P then PSPACE = EXP. Since NPSPACE = PSPACE by Savitch, as far as I can tell the underlying padding argument extends to show that $$(\tex …

It is not even known whether NC = P, but P-complete problems seem to be inherently hard to parallelize. These include Linear Programming and Horn-SAT. (In contrast, problems in NC seem reasonably ea …