Is solving minesweeper NP-complete?

2 NP-completeness Kaye showed that the minesweeper puzzle is NP-complete by reducing instances of SAT (satisfiability of formulas of propositional logic) to instances of the puzzle. The SAT instances are given as circuits constructed of Boolean logic gates.

How do you proof a problem is NP-complete?

We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete. In other words, we can prove a new problem is NP-complete by reducing some other NP-complete problem to it.

Is minesweeper an NP?

Minesweeper Consistency is NP Complete Since Minesweeper Consistency has been shown to be in NP and is NP Hard, by definition, it is NP Complete.

How do you prove that the SAT is NP-complete?

Proof of NP-Completeness Given a circuit and a satisfying set of inputs, one can compute the output of each gate in constant time. Hence, the output of the circuit is verifiable in polynomial time. Thus Circuit SAT belongs to complexity class NP.

Is there an algorithm for Minesweeper?

Thus, despite not being NP-complete, solving a consistent game of Minesweeper is still computationally difficult. Early algorithms developed to solve Minesweeper focus on the deterministic deductions needed to uncover safe moves.

Can NP-complete problems be solved in polynomial time?

The main thing to take away from an NP-complete problem is that it cannot be solved in polynomial time in any known way. NP-Hard/NP-Complete is a way of showing that certain classes of problems are not solvable in realistic time.

Is 3-SAT NP-complete?

3-SAT is NP-Complete because SAT is – any SAT formula can be rewritten as a conjunctive statement of literal clauses with 3 literals, and the satisifiability of the new statement will be identical to that of the original formula.

What is meant by NP-complete problem?

NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.

Is satisfiability problem NP-complete?

The satisfiability problem (SAT) is to determine whether a given boolean expression is satisfiable. We can view SAT as the language { E | E is the encoding of a satisfiable boolean expression }. In 1971 using a slightly different definition of NP-completeness, Steven Cook showed that SAT is NP-complete.

Is circuit satisfiability NP-complete?

We will prove that the circuit satisfiability problem CSAT described in the previous notes is NP-complete. Proving that it is in NP is easy enough: The algorithm V () takes in input the descrip- tion of a circuit C and a sequence of n Boolean values x1,… xn, and V (C, x1,…,xn) = C(x1,…,xn).

How do you complete Minesweeper?

To win a round of Minesweeper, you must click on the board every square that doesn’t have a mine under it. Once you’ve done so, the game will be over. If you accidentally click a square that has a mine beneath it, the game will be over. You’ll have the option of starting a new game or redoing the one you just played.