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Problem Detail: It’s probably possible to prove that P ≠ NP, that one-way functions exist, and that parity games cannot be solved in polynomial time (yes, I’ve been reading through this list), but how would we go about proving any of Read More …

Problem Detail: So if k is the number of tapes, is a multi-tape Turing machine allowed to have k = ∞ tapes. I’d assume not since this would give an infinite transition function? Asked By : Ozal Answered By : A.Schulz You need Read More …

Problem Detail: I want to denote the class of problems solvable by linear space multi-tape Turing machines. I have seem in many places this class being denoted by $SPACE(n)$. But why is the notation $SPACE(O(n))$ not preferred in this case? In Read More …

Problem Detail: Are all Deterministic Finite Automatons also Non Deterministic Finite Automatons? Asked By : user2441151 Answered By : Yuval Filmus That depends on how pedantic you are. Morally and semantically speaking, every DFA is an NFA in which there is a unique Read More …

Problem Detail: I have been scratching my head to find good counter examples to the following problem: Suppose we are given a directed graph G=(V,E) in which every edge has a distinct positive edge weight. A directed graph is acyclic if Read More …

Problem Detail: Dijkstra, in his essay On the cruelty of really teaching computing science, makes the following proposal for an introductory programming course: On the one hand, we teach what looks like the predicate calculus, but we do it very differently Read More …

Problem Detail: Given a string S of length n characters, is it possible to calculate the Hash of its substring [i, j] (From index i to index j. Inclusive) in O(1) using some form of precomputation ? Maybe a modification of Read More …

Problem Detail: In Andrew W. Appel’s book, Modern Compiler Implementation in ML, he says under chapter 17 that Computability theory shows that it will always be possible to invent new optimizing transformations and proceeds to prove that a fully optimizing compiler Read More …

Problem Detail: Suppose we have an algorithm like: n = 0 REPEAT c = randomInt(0,1) n = n + 1 UNTIL (c == 0) RETURN n (Assumuing the random number generator produces “good” random numbers in the mathematical sense.) I understand Read More …

Problem Detail: My Problem is: to define a “repeat until”-construct in terms of Denotational semantics. I made an attempt and now i need to know if i made it right. The Conditions are: i used the language “While” as specified in Read More …