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The primality example above, for instance, is an example of a decision problem as it can be represented by the yes–no question "is the natural number prime". In terms of the theory of computation, a decision problem is represented as the set of input strings that a computer running a correct algorithm would answer "yes" to.
NP is a class of decision problems; the analogous class of function problems is FNP. The only known strict inclusions come from the time hierarchy theorem and the space hierarchy theorem , and respectively they are N P ⊊ N E X P T I M E {\displaystyle {\mathsf {NP\subsetneq NEXPTIME}}} and N P ⊊ E X P S P A C E {\displaystyle {\mathsf {NP ...
For example, consider the problem of primality testing. The instance is a number (e.g., 15) and the solution is "yes" if the number is prime and "no" otherwise (in this case, 15 is not prime and the answer is "no"). Stated another way, the instance is a particular input to the problem, and the solution is the output corresponding to the given ...
Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of simple problem solving (SPS) addressing one issue, whereas the latter is complex problem solving (CPS) with multiple interrelated obstacles. [1]
The most frequently used method is querying experts. There exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions. [9] [10] [11] Another method is to construct the knowledge space by explorative data analysis (for example by item tree analysis) from data.
Given a function that accepts an array, a range query (,) on an array = [,..,] takes two indices and and returns the result of when applied to the subarray [, …,].For example, for a function that returns the sum of all values in an array, the range query (,) returns the sum of all values in the range [,].
An example is the meta-object protocol in Smalltalk and CLOS that gives developers runtime access to the class objects and enables them to dynamically redefine the structure of the knowledge base even at runtime. Meta-representation means the knowledge representation language is itself expressed in that language.
Range minimum query reduced to the lowest common ancestor problem.. Given an array A[1 … n] of n objects taken from a totally ordered set, such as integers, the range minimum query RMQ A (l,r) =arg min A[k] (with 1 ≤ l ≤ k ≤ r ≤ n) returns the position of the minimal element in the specified sub-array A[l …