Problem Detail: I am trying to teach myself different approaches to software verification. I have read some articles. As far as I learned, propositional logic with temporal generally uses model checking with SAT solvers (in ongoing – reactive systems), but what Read More …
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[Solved]: Vapnik-Chervonenkis Dimension: why cannot four points on a line be shattered by rectangles?
Problem Detail: So I’m reading “Introduction to Machine Learning” 2nd edition, by Bishop, et. all. On page 27 they discuss the Vapnik-Chervonenkis Dimension which is, “The maximum number of points that can be shattered by H [the hypothesis class] is called Read More …
[Solved]: Proving that NPSPACE $subseteq$ EXPTIME
Problem Detail: I am following “Introduction to the theory of computation” by Sipser. My question is about relationship of different classes which is present in Chapter 8.2. The Class PSPACE. $P subseteq NP subseteq PSPACE = NPSPACE subseteq EXPTIME$ I am Read More …
[Solved]: Use closure properties to transform languages to $L := { a^nb^n : nin mathbb N }$
Problem Detail: For the purpose of proving that they are not regular, what closure properties can I use to transform the languages $L_a = { a^*cw mid w in {a,b }^* land |w|_a = |w|_b }$ and $L_b = {ab^{i_1}ab^{i_2}ldots ab^{i_n} Read More …
[Solved]: Proof of equivalence of parse-trees and derivations
Problem Detail: Intuitively, every derivation in a context-free grammar corresponds to a parse-tree and vise versa. Is this intuition correct? If so how can I formalize and prove such a thing? Asked By : saadtaame Answered By : saadtaame Theorem. Let $G = Read More …
[Solved]: Equality of NSpace and coNSpace classes
Problem Detail: I’m trying to decide which of the following statements are true: $mathsf{NSpace}(log log n) = mathsf{coNSpace}(log log n )$ $mathsf{NSpace}(lg^2n) = mathsf{coNSpace}(lg^2n)$ $mathsf{NSpace}(sqrt n) = mathsf{coNSpace}(sqrt n)$ I thought immediately that (1) is correct since $lg lg n < Read More …
[Solved]: What is a Turing Machine in class coNP
Problem Detail: On the wikipedia article about the polynomial hierarchy http://en.wikipedia.org/wiki/Polynomial_hierarchy it says “$A^B$ is the set of decision problems solvable by a Turing machine in class A augmented by an oracle for some complete problem in class B” What is Read More …
[Solved]: Deciding the set of all Turing machines that halt in at most $k|x|$ steps $forall x in Sigma^*$
Problem Detail: Let $L = { <M> | M$ halts on every input $x$ in at most $200 * |x|$ steps $}$. Is $L$ decidable? Recognizable? Given that membership in $L$ asserts something about $M$’s behavior on an infinite set of Read More …
[Solved]: lexicographic depth-first search complexity class
Problem Detail: It seems to me to be incorrect to say that lexicographic DFS is P-complete, since it isn’t a decision problem. There is a corresponding decision problem, first DFS ordering, which is known to be P-complete. However, I want to Read More …
[Solved]: Genetic Algorithm Minimum Population Size
Problem Detail: Is there a minimum limit to a pool (population) size when using the genetic algorithm to solve an optimization problem? For example a population of size 2. Asked By : Declan Murphy Answered By : Philippe Olivier I had a similar Read More …
