# Shitikanth

 Oct 8 awarded Critic Oct 8 awarded Citizen Patrol Oct 8 comment Solving the recurrence T(n) = T(n/2) + T(n/4) + T(n/8)?This is a homework problem from an active assignment from this course. Voted to close. Aug 28 revised Deciding if language is Context-Freeadded 4 characters in body Aug 28 revised Deciding if language is Context-FreeChanged $L_1$ to $L$ Aug 28 answered Deciding if language is Context-Free Aug 27 answered Power series $\sum n^3a_nz^n$ Aug 27 comment Counting QuestionNo, I'm pretty sure their solution is incorrect. For this question, there is no need to count at all, see my answer. Aug 27 answered Counting Question Aug 27 comment Counting QuestionThe textbook's answer seems to be wrong. $|A| = {5 \choose 1} 2! {25 \choose 2} 3! {8 \choose 3} {4 \choose 1}$ = 4,032,000. Aug 27 awarded Yearling Aug 27 awarded Autobiographer Aug 27 comment Complex number inequality, $|e^{z_1}-e^{z_2}| \leq |z_1 - z_2|$ if $Re(z_1),Re(z_2) \leq 0$You should probably start with proving $|e^z - 1| \le |z|$ for $Re(z) \le 0$. Aug 26 comment If $f(x)$ is an integrable function, can we always find its anti-derivative using ordinary methods of integration?Do you have any constraints on what substitutions are allowed? If $\int f (x) dx = g(x)$ where g(x) is an elementary function, you can always substitute $y = g(x)$ to get $\int f(x) dx = \int dy = g(x) + const$. Aug 26 revised Formal language without grammardeleted 3 characters in body; added 1 characters in body Aug 26 answered Formal language without grammar Aug 26 comment Formal language without grammarWhenever you have a question about grammars, the Dragon book is a good place to look. Aug 25 comment Is there any programming language in which any equivalent program has a unique, decidable normal representation?To add to my previous comment, I think propositional logic is powerful enough to express CFGs so your requirements can not be met. Aug 25 comment Is there any programming language in which any equivalent program has a unique, decidable normal representation?Regular expressions is such a "programming language". Given a regular expression you can find a unique minimal DFA that accepts the words matching the regular expression and you can use this to check if two regular expressions are equivalent. On the other hand, testing the equivalence of two context free grammars is undecidable. So any such programming language would not have the power to write parsers for a general CFG. Aug 24 answered Calculation of volume and centre of mass of an arbitrary polyhedron