Computation and languages, Theory of Computation

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.

Posted Date: 3/20/2013 5:50:25 AM | Location : United States







Related Discussions:- Computation and languages, Assignment Help, Ask Question on Computation and languages, Get Answer, Expert's Help, Computation and languages Discussions

Write discussion on Computation and languages
Your posts are moderated
Related Questions
constract context free g ={ a^n b^m : m,n >=0 and n


Describe the architecture of interface agency


The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo

Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N

proof ogdens lemma .with example i am not able to undestand the meaning of distinguished position .

Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a

what exactly is this and how is it implemented and how to prove its correctness, completeness...

While the SL 2 languages include some surprisingly complex languages, the strictly 2-local automata are, nevertheless, quite limited. In a strong sense, they are almost memoryless