PROBLEM OF DETERMINING WHETHER A GIVEN PROGRAM WILL FINISH RUNNING OR CONTINUE FOREVER
The halting problem; Halt problem; Halting predicate; Turing's halting theorem; Halting Problem; Halting Theorem; Determining whether a program is going to run forever; Turing's halting problem; Lossy Turing machine
The problem of determining in advance whether a particular
program or algorithm will terminate or run forever. The
haltingproblem is the canonical example of a {provably
unsolvable} problem. Obviously any attempt to answer the
question by actually executing the algorithm or simulating
each step of its execution will only give an answer if the
algorithm under consideration does terminate, otherwise the
algorithm attempting to answer the question will itself run
forever.
Some special cases of the haltingproblem are partially
solvable given sufficient resources. For example, if it is
possible to record the complete state of the execution of the
algorithm at each step and the current state is ever identical
to some previous state then the algorithm is in a loop. This
might require an arbitrary amount of storage however.
Alternatively, if there are at most N possible different
states then the algorithm can run for at most N steps without
looping.
A program analysis called termination analysis attempts to
answer this question for limited kinds of input algorithm.
(1994-10-20)
Haltingproblem
PROBLEM OF DETERMINING WHETHER A GIVEN PROGRAM WILL FINISH RUNNING OR CONTINUE FOREVER
The halting problem; Halt problem; Halting predicate; Turing's halting theorem; Halting Problem; Halting Theorem; Determining whether a program is going to run forever; Turing's halting problem; Lossy Turing machine
In computability theory, the haltingproblem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the haltingproblem for all possible program-input pairs cannot exist.
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.