A message from our CEO about the future of Stack Overflow and Stack Exchange. Read now.

# Questions tagged [reductions]

In computability and complexity, finding mappings between problems that allow solving one problem using a solution of another one. For reduction in programming language theory (e.g. beta-reduction), see [lambda-calculus] or [term-rewriting].

943 questions
Filter by
Sorted by
Tagged with
50 views

### Variant of TSP: allow each vertex to be visited at most twice

We are given a finite set $V$ and a set of distance $d : V\times V \rightarrow R\ge 0$ and we wish to compute a tour. Suppose we allow each vertex to be visited at most twice in the tour. How can we ...
123 views

### Is finding a minimal set of seed variables for a complete deduction of a system of equations NP-complete?

Suppose we have a set of variables $V$. We also have a set of equations $E$, which are sets of at least two variables. We don't know anything about these equations, except if we know all but one of ...
542 views

### Halting problem in EXP-complete

I have some troubles understanding why the halting problem is in EXP. In Wikipedia the following is written: It is in EXPTIME because a trivial simulation requires O(k) time, and the input k is ...
55 views

### A doubt on converting NOT gate to CNF formula

For a NOT gate if $x_1$ is input and $x_2$ is the corresponding output, I see the equivalent CNF (conjunctive normal form) is $(x_1 \lor x_2) \land (\overline x_1 \lor \overline x_2)$. My ...
38 views

291 views

### How to solve the optimization of bin packing using the decision version

Let us say the optimization version of the bin packing problem asks you to give a packing using the fewest bins possible and the decision version asks if it is possible to pack the bins into $k$ bins. ...
24 views

### Two (oracle) turing machines producing the same language

I need to solve the question if two given oracle turing machines M$_{1}$ and M$_{2}$ have the same language, so T(M$_{1}$) = T(M$_{1}$). An oracle turing machine can use such an oracle for deciding ...
108 views

### Reduction from Exact Cover to Fixed Exact Cover

I am trying to reduce Exact Cover to Fixed Exact Cover to show that Fixed Exact Cover is NP-Hard. Exact Cover Input S = {x1, x2, ..., xn} (set) P = {P1, P2, ..., Pm} (subsets of S) Decision ...
59 views

### Parity Hamiltonian path problem

Wikipedia says that Hamiltonian path problem is NPC, but Parity Hamiltonian path problem (i.e., is there an odd amount of hamiltonian path) is P. Does a reduction from, e.g., SAT, to HPP, unavoidably ...
48 views

### Prove disprove an existence of mapping reduction between 2 sets

I am currently studying mapping reduction in computational theory and finding it hard to grasp the concept fully. For reference, consider the following given WHILE-Prog sets: A = { (p.d) | p doesn'...
19 views

38 views