hi, Thanks for the replies,a few more queries.
> Complete means that we can take any and all -legal- > strings within that > formalism and assign them -one of only two- truth > values; True v False. > > The fundamental problem is axiomatic. The rules > define -all- statements as > being -either true or false-, no other possibility > is allowed -by > principle-. By principle of what? > > We create two lists 'true' and 'false', we are > -required- to put -any- > string (or formula in Godel-speak, or 'sequence' and > 'inside or outside' > with regard to Cauchy Completeness) we write in one > of these two, and > only these two lists. > > However, as Godel shows, we -can- write strings > (some of them are quite > simple which is what makes it so shocking) that we > can't put in -either- > of these lists. > > There is -no- place to write it down. Isn't that the reason we call it 'undecidable',put it in an undeciable list which is the truth. We can actually write these symbols down,it will be true for some and false for some eg: If we say-For a context free grammar G, L(G) is ambigious.This is true for some G and false for G,If we ask a turing machine to solve this question,it can't because there is no algorithm to determine the statement is true or false. A function is turing computable only if for every element in the domain,the function's value can be computed with a Turing machine. The domain is important,for sime G we get True and some G we get false.By the defenition of turing complenetess,since we cannot show it is true or false for every element in the domain,it is not turing computable and hence undecidable.We can write down the symbols but it does n't mean any thing. Regards Sarath. __________________________________________________ Do you Yahoo!? Yahoo! Mail Plus - Powerful. Affordable. Sign up now. http://mailplus.yahoo.com
