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Reduction maximum independent set to MIS in a very dense graph

We got a reduction maximum independent set to MIS in a very dense graph, or alternatively negative monotone 2-CNF to MAX-ONEs with a formula with many clauses. Let $G$ be graph of order $n$ and ...
joro's user avatar
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3 votes
1 answer
708 views

Is strictly harder than NP-hard cryptography possible?

Looks like there is cryptography based on NP-hard problem, e.g. McEliece cryptosystem. The algorithm is an asymmetric encryption algorithm and is based on the hardness of decoding a general linear ...
joro's user avatar
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16 votes
4 answers
1k views

Representing mathematical statements as SAT instances

The following problem (call it THEOREMS) belongs to class NP. Input: Mathematical statement $S$ (written in some formal system such as ZFC) and positive integer $n$ written in unary. Output: "Yes" if ...
Bogdan's user avatar
  • 781
1 vote
1 answer
310 views

Counterexamples for this algorithm for recognizing lexicographic product of graphs?

Found a possible reduction from recognizing lexicographic product of graphs to 2SAT (since 2SAT is polynomial, the algorithm is polynomial). Can't prove completeness of the algorithm and since it is ...
joro's user avatar
  • 25.4k
1 vote
0 answers
89 views

Deciding / Approximating Parity of Small Depth Decision Trees

Let C be a circuit such that: C: $\{0,1\}^n$ to $\{0,1\}$ the top most gate is a parity gate all the inputs to the parity gate are small depth decision trees there is a total of $2^{ log^k n}$ ...
user22209's user avatar