Computation and languages, Theory of Computation

Assignment Help:

When we study computability we are studying problems in an abstract sense. For example, addition is the problem of, having been given two numbers, returning a third number that is their sum. Two problems of particular interest in Computer Science, which you have probably encountered previously, are the Traveling Salesperson Problem (TSP) and the Halting Problem. In TSP one is given a list of distances between some number of cities and is asked to ?nd the shortest route that visits each city once and returns to the start. In the Halting Problem, one is given a program and some appropriate input and asked to decide whether the program, when run on that input, loops forever or halts. Note that, in each of the cases the statement of the problem doesn't give us the actual values we need to provide the result for, but rather just tells us what kind of objects they are. A set of actual values for a problem is called an instance of the problem. (So, in this terminology, all the homework problems you did throughout school were not problems but were, rather, instances of problems.)

A problem, then, speci?es what an instance is, i.e., what the input is, and how the solution, or output, must be related to the that input.
There are a number of things one might seek to know about a problem, among them:

• Can it be solved algorithmically; is there a de?nite procedure that solves any instance of the problem in a ?nite amount of time? Inother words, is it computable. Not all problems are computable; the halting problem is the classic example of one that is not.

• How hard is it to solve? What kind of resources are needed and how much of those resources is required? Again, some problems are harder than others. TSP is an example of a frustrating class of problems that have no known e?cient solution, but which have never been proven to be necessarily hard.


Related Discussions:- Computation and languages

Pendulum Swings, how many pendulum swings will it take to walk across the c...

how many pendulum swings will it take to walk across the classroom?

Regular expressions, The project 2 involves completing and modifying the C+...

The project 2 involves completing and modifying the C++ program that evaluates statements of an expression language contained in the Expression Interpreter that interprets fully pa

Answer, And what this money. Invovle who it involves and the fact of,how we...

And what this money. Invovle who it involves and the fact of,how we got itself identified candidate and not withstanding time date location. That shouts me media And answers who''v

Positiveness problem - decision problems, For example, the question of whet...

For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that

Exhaustive search, A problem is said to be unsolvable if no algorithm can s...

A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note

Path function of a nfa, The path function δ : Q × Σ*→ P(Q) is the extension...

The path function δ : Q × Σ*→ P(Q) is the extension of δ to strings: Again, this just says that to ?nd the set of states reachable by a path labeled w from a state q in an

Operations on strictly local languages, The class of Strictly Local Languag...

The class of Strictly Local Languages (in general) is closed under • intersection but is not closed under • union • complement • concatenation • Kleene- and positive

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd