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Questions related to the (computational) complexity of solving problems

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 …
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 …
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- …
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 …
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 $U=${$a_1, a … asked Mar 22 '12 by Mohammad Al-Turkistany 0answers If we consider polynomial-time (or log-space) computable reductions$<_p^m$as transformations between computational problems, then the following definitions of known complexity classes suggest the c … asked Nov 20 '13 by Mohammad Al-Turkistany 0answers The notion of low information content is used to describe sparse sets and tally sets in complexity theory. Such sets can not be$NP$-complete unless$P=NP$. I am not aware of a formal information-theo … asked Nov 23 '14 by Mohammad Al-Turkistany 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 = …
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 $R … asked Aug 26 '16 by Mohammad Al-Turkistany 1answer This question is motivated by my answer to another question in which I stated the fact that both Betweeness and Non-Betweeness problems are$NP$-complete. In the former problem there is a total order … asked Apr 18 '12 by Mohammad Al-Turkistany 1answer I know that maximum independent set on cubic triangle-free graphs is NP-complete. Is it still NP-complete in case we require the independent set to be of size exactly$|V|/2$? Basiclly, YES instanc … asked Feb 7 '13 by Mohammad Al-Turkistany 1answer Clique problem is a well known$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$is … asked Nov 25 '13 by Mohammad Al-Turkistany 1answer It is common to define$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 …