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Results tagged with reductions
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user 109
A reduction is the transformation of one problem into another problem. A example of using a reduction would be to be to show if a problem P is undecidable. This would be achieved by transforming or performing a reduction of a decision problem $P$ into an undecidable problem. If this can be achieved then we have shown that this problem P is undecidable.
13
votes
Nontrivial membership in NP
My favourite example is a classic 1977 result of Ashok Chandra and Philip Merlin. They showed that the query containment problem was decidable for conjunctive queries. The conjunctive query containm …
- 19.2k
4
votes
Nontrivial membership in NP
Deciding reachability for various kinds of infinite-state systems is sometimes decidable, often not. For some interesting special cases a small enough and efficiently checkable certificate always exi …
- 19.2k
13
votes
3
answers
345
views
Can limit of hard languages be easy?
Can the following all hold simultaneously?
$L_s$ is contained in $L_{s+1}$ for all positive integers $s$.
$L = \bigcup_s L_s$ is the language of all finite words over $\{0,1\}$.
There is some comple …
- 19.2k
12
votes
1
answer
215
views
Reductions between languages of different densities?
The density of a language $X$ is a function $d_X \colon \mathbb{N} \to \mathbb{N}$ defined as $$d_X(n) = |\{x\in X \mid |x| \le n\}|.$$
Suppose $A$ and $B$ are languages over some finite alphabet, $A$ …
- 19.2k
13
votes
1
answer
3k
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Improving Cook's generic reduction for Clique to SAT?
I am interested in reducing $k$-Clique to SAT without making the instance much larger.
Clique is in NP so it can be reduced to SAT using logarithmic space.
The straightforward Garey/Johnson textbook …
- 19.2k
22
votes
1
answer
1k
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How to prove that USTCONN requires logarithmic space?
However, USTCONN being complete for L under logspace reductions does not seem to imply this. … This might then perhaps be adapted to show that USTCONN is complete for L under FO-reductions. …
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1
vote
Reduction from independent set in hypergraphs to independent set in graphs
I am not as convinced as @Andrew Morgan is that this is "fair standard fare", and would also welcome pointers to a citable reduction.
In particular, I do not see how to maintain a linear blowup if $k$ …
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