Do unsolvable problems exist?
There are some problems that a computer can never solve, even the world’s most powerful computer with infinite time: the undecidable problems. An undecidable problem is one that should give a “yes” or “no” answer, but yet no algorithm exists that can answer correctly on all inputs.
Can a Turing machine solve any problem?
Any problem that you can solve on a computer (even a quantum computer) can be solved by a Turing machine. A Turing machine can actually solve problems that no finite computer can solve, since Turing machines have unbounded memory, which real computers do not.
Which problems are not solved by any algorithm?
Problems that cannot be solved by any algorithm are called? Explanation: Problems cannot be solved by any algorithm are called undecidable problems. Problems that can be solved in polynomial time are called Tractable problems.
Why is halting problem unsolvable?
Rice’s theorem generalizes the theorem that the halting problem is unsolvable. It states that for any non-trivial property, there is no general decision procedure that, for all programs, decides whether the partial function implemented by the input program has that property.
What is unsolvable problem?
(definition) Definition: A computational problem that cannot be solved by a Turing machine. The associated function is called an uncomputable function. See also solvable, undecidable problem, intractable, halting problem.
What did the Turing machine prove?
Turing’s proof is a proof by Alan Turing, first published in January 1937 with the title “On Computable Numbers, with an Application to the Entscheidungsproblem.” It was the second proof (after Church’s theorem) of the conjecture that some purely mathematical yes–no questions can never be answered by computation; more …
Does Turing exist?
Turing’s machine is not a real machine. It’s a mathematical model, a concept, just like state machines, automata or combinational logic. It exists purely in the abstract. (Although “real” implementations of the Turing machine do exist, like in this foundational computer science paper.)
Which problem Cannot be solved by backtracking method?
Which of the problems cannot be solved by backtracking method? Explanation: N-queen problem, subset sum problem, Hamiltonian circuit problems can be solved by backtracking method whereas travelling salesman problem is solved by Branch and bound method.
How do you prove halting problems?
Theorem (Turing circa 1940): There is no program to solve the Halting Problem. Proof: Assume to reach a contradiction that there exists a program Halt(P, I) that solves the halting problem, Halt(P, I) returns True if and only P halts on I.
Can the halting problem be solved?
Halting problem is perhaps the most well-known problem that has been proven to be undecidable; that is, there is no program that can solve the halting problem for general enough computer programs.
Is it possible to solve a game with an algorithm?
However, since for many non-trivial games such an algorithm would require an infeasible amount of time to generate a move in a given position, a game is not considered to be solved weakly or strongly unless the algorithm can be run by existing hardware in a reasonable time.
Is there an unsolvable start in the game?
It’s not hard to prove that an unsolvable start exists. Just imagine a start where the only possible first moves would be moving cards to the extra cells. In some versions, -1 and -2 are examples of this though the only way to play them is to choose that seed.
What is the optimal strategy for a game-playing computer?
Although the optimal strategy of a game may not (yet) be known, a game-playing computer might still benefit from solutions of the game from certain endgame positions (in the form of endgame tablebases), which will allow it to play perfectly after some point in the game. Computer chess programs are well known for doing this.
What are some good examples of game theory being applied to games?
As an example of a strong solution, the game of tic-tac-toe is solvable as a draw for both players with perfect play (a result even manually determinable by schoolchildren). Games like nim also admit a rigorous analysis using combinatorial game theory.