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Questions related to the (computational) complexity of solving problems

1
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0answers
Turing machines were very successful in computability theory where Turing used them to resolve the Halting problem. His breakthrough led to proving that many other problems are algorithmicly undecidab …
asked Apr 15 '16 by Mohammad Al-Turkistany
1
vote
1answer
Horn3SAT is $P$-complete problem under logspace reductions. Since Horn3SAT is in $P$ its complement must have short witnesses. I am looking for natural short proof that a Horn3SAT formula is not satis …
asked Aug 9 '15 by Mohammad Al-Turkistany
1
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0answers
I am interested in all know classes of Computatinal problems. The Wikipedia article on computational problems types is incomplete. Some of the known classes are: 1- Decision problem such as 3SAT 2- …
asked Jun 14 '18 by Mohammad Al-Turkistany
1
vote
2answers
I am not an expert in Zero-knowledge proofs and I am interested in its applicability to general mathematical proofs. Suppose we're willing to assume that NP-complete problems are intractable and requ …
asked Mar 3 '16 by Mohammad Al-Turkistany
2
votes
2answers
Many intractable $NP$-complete problems can be modeled as deciding whether a set of triples, $F=${$t_1, t_2, ..., t_n$} where each triple $t_i$ is a subset of three elements over base set $U=${$a_1, a …
asked Mar 22 '12 by Mohammad Al-Turkistany
2
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0answers
If we consider polynomial-time (or log-space) computable reductions $<_p^m$ as transformations between computational problems, then the following definitions of known complexity classes suggest the c …
asked Nov 20 '13 by Mohammad Al-Turkistany
1
vote
0answers
The notion of low information content is used to describe sparse sets and tally sets in complexity theory. Such sets can not be $NP$-complete unless $P=NP$. I am not aware of a formal information-theo …
asked Nov 23 '14 by Mohammad Al-Turkistany
5
votes
1answer
The PCP theorem implies (with other results) that there is no polynomial time algorithm for MAX 3SAT to find an assignment satisfying $7/8+ \epsilon$ clauses of a satisfiable 3SAT formula unless $P = …
asked Jun 26 '13 by Mohammad Al-Turkistany
3
votes
1answer
I am interested in combinatorial (worst-case) one-way functions. I came across this problem which may be related to coding theory problems (I am not an expert in coding theory). INPUT: Two vectors $R …
asked Aug 26 '16 by Mohammad Al-Turkistany
4
votes
1answer
This question is motivated by my answer to another question in which I stated the fact that both Betweeness and Non-Betweeness problems are $NP$-complete. In the former problem there is a total order …
asked Apr 18 '12 by Mohammad Al-Turkistany
11
votes
1answer
I know that maximum independent set on cubic triangle-free graphs is NP-complete. Is it still NP-complete in case we require the independent set to be of size exactly $|V|/2$? Basiclly, YES instanc …
asked Feb 7 '13 by Mohammad Al-Turkistany
14
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1answer
Clique problem is a well known $NP$-complete problem where the size of the required clique is part of the input. However, k-clique problem has a trivial polynomial time algorithm ($O(n^k)$ when $k$ is …
asked Nov 25 '13 by Mohammad Al-Turkistany
6
votes
1answer
It is common to define $P$-completeness with respect to logspace many-one reductions. I am looking for a complexity class $C$ such that if $C=P$ then all problems in $P$ are $P$-complete under many-on …
asked Jan 24 '15 by Mohammad Al-Turkistany
0
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Some computational problems have different complexity on different graph classes. For instance, 3-edge coloring is NP-complete on cubic graphs but polynomial on cubic bipartite graphs. What are th …
asked Dec 27 '17 by Mohammad Al-Turkistany
4
votes
1answer
I am aware that deciding the existence of decomposition of a cubic graph into edge-disjoint claws is polynomial time solvable. Since a cubic graph has a decomposition into edge-disjoint claws if and o …
asked Jul 27 '15 by Mohammad Al-Turkistany

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