# Questions tagged [polynomial-time]

Use for algorithms, algorithm-analysis and complexity-theory questions that aim for polynomial running time resp. time complexity. Such questions often are are reference-requests or about runtime-analysis or time-complexity.

32 questions with no upvoted or accepted answers
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### P vs NP and the Time Hierarchy

Assuming $P\neq NP$, is it possible that there exists a $k$ such that $P\subseteq\textsf{NTIME}(t^k)$? There reason I ask this is that I assume the following: P=NP \implies \forall k\ \exists j.\ \...
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### Linear time reduction equivalence

I have to show if the following statement is true or false. Suppose we have two problems $A$ and $B$. We want to know whether the following is true: If $A \le_p B$ and there is an algorithm which ...
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### Are there any RE-complete languages w.r.t. polynomial reduction?

I need to decide if there exists $L\in RE$ so that for every $L'\in RE$ we have $L' \leqslant_p L$, meaning a polynomial-time reduction. I've tried to use $L=A_{TM}$ (the accepting problem), but got ...
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### Proving languages are complete on NL?

I'm trying to prove that every language that is not the empty set or {0,1}* is complete for NL (nondeterministic logarithmic space) under polynomial-time Karp reductions. I'm really not sure how to ...
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### Nash Equilibrium in Tree of Bounded Degree

I have an exercise which I can't solve. Exercise. Consider a game where the players have $2$ pure strategies each and assume that the graph $G$ is a tree with maximum degree $3$. Give a polynomial ...
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### Is $P^{SAT}=NP \cup coNP$

I have a following problem: Let $P^{SAT}$ be a class of problems decidable by a deterministic polynomial Turing Machines with SAT oracle. (only one question to oracle). Assume that: \$coNP \neq NP ...