Problem Detail: Philip Wadler has written a brilliant paper called ‘Theorems for Free’. The big idea is that you can use types to reason about your program, and even prove simple theorems about your program. We see these ideas about types Read More …
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[Solved]: Is this NIM game tree correct?
Problem Detail: I have an assignment to construct a game of Nim (a game in which two players must divide a pile of tokens into two unequal sizes; 6 can be divided into 2 & 4 but not 3 & 3). Read More …
[Solved]: What is OUTER UNION and why is it partially compatible
Problem Detail: I am trying to understand how a OUTER UNION $∪^✳$ works, and why it is only partially compatible. I am aware this operation was created to take union of tuples from two relations if the relation are not type Read More …
[Solved]: Is finding a solution of a satisfiability problem harder than deciding satisfiability?
Problem Detail: Is the problem of determining whether or not a given Boolean expression is satisfiable computationally distinct from actually finding a solution to the expression? In other words, is there another way of finding that a given expression is satisfiable Read More …
[Solved]: Origins of the term “distributed hash table”
Problem Detail: I am currently researching for my diploma thesis in computer science with a topic in the area of distributed hash tables. Naturally, I came to the question were the term distributed hash table came from. (I know it is Read More …
[Solved]: Why does many to one reduction imply Turing reducibility?
Problem Detail: So, $ Aleqslant_mB $ (many to one reduction) means that language $A$ can be reduced to language $B$ if there exists a Turing-calculable function $f$ so $ f(A) subseteq B$ and $ f(overline{A}) subseteq overline{B} $. $ Aleqslant_TB $ Read More …
[Solved]: Proving Regularity of Languages that are 1/k of an already known regular language
Problem Detail: There is this question in Kozen, that states if a language is regular then the first half would also be regular. Also I found a material on the internet that extends the thinking saying a language that is two-thirds Read More …
[Solved]: Algorithm – Wine Bottle Filling
Problem Detail: You have two friends, call them A and B. They each are given two wine bottles: one bottle holds k_1 litres and the other k_2 litres. Both A and B can perform these operations: – completely fill a wine Read More …
[Solved]: Clique decision problem restricted to a subgraph
Problem Detail: I know that the clique problem is NP-complete. However, what if we change the problem a little bit? For example, Given a graph $G(V,E)$, an integer $k$ and a subset $S$ of $m$ vertices, we are given a decision Read More …
[Solved]: If $L$ is a regular language, how to prove $L_1 = { uv mid u in L, |v| =2 }$ is also regular?
Problem Detail: If $L$ is a regular language, prove that the language $L_1 = { uv mid u in L, |v| =2 }$ is also regular. My idea: $L$ can be represented as a DFA and then you could add Read More …
