Questions in Theory of Computation Assignment Example | Topics and Well Written Essays - 750 words

Questions in Theory of Computation - Assignment Example The binary search uses the divide and conquer algorithm. Dynamic programming solves a complex problem by breaking it down into easier sub-problems hence it solves each sub-problem once only, reducing number of computations and can solve optimization problems that would not have been easily sorted out through greedy approach since the greedy algorithm works in phases and at each phase, it gets the best at that instance with no regard of others. Backtracking tries different solutions till it finds a solution that is more suitable. Such problems can only be solved by trying every possible configuration and each configuration is tried only once. This describes the restraining behavior of a function when an argument leans to a value or to infinity and is used to describe a function according to their growing rates and functions with identical growth are denoted with the same expression A language is in class P if there is a deterministic Turing machine such that the TM runs for polynomial time over all inputs and for all values of the language, the TM outputs 1 and for all values in the language, the TM outputs 0.A problem is in a complex class P when there is an algorithm that solves it in a time bounded by polynomial of the input size, hence there will be an algorithm that will tell in a polynomial time whether a given number is composite S is NP-hard if, for every S ∈ NP, S, hence implying that S is ‘as hard as’ all the problems in NP while a problem S is NP-complete if it is NP-hard and it is also in the class NP itself. In symbols, S is NP-complete if S is NP-hard and S ∈ NP. NP-complete problem forms a set of problems that could be intractable or tractable. This is a case where it is not possible to check the validity of either a yes –answer or a no-answer in a finite amount of time. For the case of an asserted no-answer, the argument that establishes that can be no finite