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 …
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[Solved]: Is 2-SAT with XOR-relations NP-complete?
Problem Detail: I’m wondering if there is a polynomial algorithm for “2-SAT with XOR-relations”. Both 2-SAT and XOR-SAT are in P, but is its combination? Example Input: 2-SAT part: (a or !b) and (b or c) and (b or d) XOR Read More …
[Solved]: What will i obtain if i apply a xor-ing a one way function and it’s input?
Problem Detail: I know that a one-way function is informally a function that it’s easy to compute but hard to invert. If f(x) is a one way function the function $g(x) = xoplus f(x)$ is a one-way function? My intuition is Read More …
[Solved]: Finding a winning strategy for toads and frogs
Problem Detail: Recently I got interested in a game called Toads and Frogs and I’m trying my best to come up with some software which would be able to beat an average (i.e. not knowing the strategy) human though I’m struggling Read More …
[Solved]: Derive a Context Free Grammar from a language
Problem Detail: I am having challenges (in two phases) with creating a CFG. Derive the CFG for the following language Show parse trees for the strings cacab and aacabbb obtained from the grammar designed above. I am getting a bit mixed Read More …
[Solved]: Is this finite graph problem decidable? What factors make a problem decidable?
Problem Detail: I want to know if the following problem is decidable and how to find out. Every problem I see I can say “yes” or “no” to it, so are most problems and algorithms decidable except a few (which is Read More …
[Solved]: Reconciling NP and the decision problem
Problem Detail: So I’ve seen that most NP-Complete problems seem to take the form of decision problems – problems which require only a yes/no answer. However, how can this be reconciled with the requirement that the solution of an NP problem Read More …
[Solved]: Proving closure under complementation of languages accepted by min-heap automata
Problem Detail: This is a follow-up question of this one. In a previous question about exotic state machines, Alex ten Brink and Raphael addressed the computational capabilities of a peculiar kind of state machine: min-heap automata. They were able to show Read More …
[Solved]: Visualize Graph Clusters
Problem Detail: I am working on my thesis which involves using ant based techniques for graph clustering. I am testing the algorithm currently and I was wondering if there is a way that I can visualize the clusters of a given Read More …
[Solved]: Is it possible to prove thread safety?
Problem Detail: Given a program consisting of variables and instructions which modify these variables, and a synchronization primitive (a monitor, mutex, java’s synchronized or C#’s lock), is it possible to prove that such a program is thread safe? Is there even Read More …
