Problem Detail: I’ve been trying to investigate 3-SAT for variables appearing 3 times and so far I’m getting some mixed answers as to its complexity. For example, https://people.maths.ox.ac.uk/scott/Papers/restricted3sat.pdf says instances of 3-SAT in which every variable occurs three times are always Read More …
Author: ignougroup
[Solved]: Prove that context free languages are not closed under swapping prefixes and suffixes
Problem Detail: Prove that context free languages aren’t closed under this operation: $ A(L) = { zyx mid x,y,z in {0,1 }^*, xyz in L } $ Obviously, we need to find a context free language $L$ such that $A(L)$ isn’t Read More …
[Solved]: Types as first class Citizen
Problem Detail: Coming from a C++ background I don’t understand why one needs types / type expressions as first class citizen? The only language I know that supports this feature is Aldor. Does anybody have some literature about types as first Read More …
[Solved]: How to solve this Planning Domain Definition Language (PDDL) question?
Problem Detail: These are 5 action descriptions with conditional effects: Action(A, Precond:{X}, Effect:{when P : ~X), Z}) Action(B, Precond:{Y}, Effect:{when Z : ~P), ~Y,~Z,X}) Action(C, Precond:{~Z}, Effect:{when P : ~X), Y}) Action(D, Precond:{~X}, Effect:{when Q : X)}) Action(E, Precond:{Z}, Effect:{when Q Read More …
[Solved]: Proving that Turing Machine M runs in time $O(2^{dn})$
Problem Detail: I’m trying to solve this question in order to review for my exam, and this one has got me a bit stumped. From the looks of it, it seems like a fairly straight-forward question, but I can’t figure out Read More …
[Solved]: Is there a more efficient algorithm than backtracking/dynamic programming?
Problem Detail: Consider the following game: One day a castle is attacked at sunrise (by surprise) by n soldiers. Each soldier carries a canon and a rifle. The castle has strength s. On the first day each soldier shoots his canon Read More …
[Solved]: Help interpreting this deadlock question
Problem Detail: I have this assignment question but I am a bit unsure how to go about answering it. The question is as follows and accompanied by the image below: Three processes are competing for six resources labelled A to F Read More …
[Solved]: Do problems in P have a minimum number of YES and NO instances?
Problem Detail: If a decision problem A belongs to the polynomial complexity class P, must there be at least one YES instance and one NO instance of the problem? I know that in the definition of a Turing machine an accept Read More …
[Solved]: Which class of languages is accepted by PDA when we restrict the stack to logarithmic size?
Problem Detail: Let $mathrm{LOG}_{mathrm{CF}}$ be the class of all languages recognized by a Pushdown-automaton that uses $leq log n$ cells of its stack for each input of length $n$. Obviously, this class is a proper subset of the class of context-free Read More …
[Solved]: Without using pumping lemma, can we determine if $A ={ww mid w in {0,1}^* }$ is non regular?
Problem Detail: Without using pumping lemma, can we prove $A ={ww mid w in {0,1}^* }$ is non regular? Is $L= {w mid w in {0,1}^* }$ non regular? I’m thinking of using concatenation to prove the former isn’t regular. If Read More …
