Problem Detail: I am studying formal language theory and have been asked to prove the following: $forall L, L^*=(L^*)^*$ I’ve started with $def. L^* = bigcup_{i in mathbb{N}} L_i, L_0={{epsilon}}, L_1={L}, L_{i+1}={uv|uin L_i, vin L}$ $then (L^*)^* = bigcup_{i in mathbb{N}} Read More …
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[Solved]: Is Big-Oh notation preserved under monotonic functions?
Problem Detail: I was just looking at the big-Oh notation. I wanted to know if the following is true in general $$f(n)=O(g(n)) implies log (f(n)) = O(log (g(n)))$$ I can prove that this is true if $g$ is monotonically increasing, but Read More …
[Solved]: Can the encodings set of a non-trivial class of languages which contains the empty set be recursively enumerable?
Problem Detail: Let $C$ be a non-trivial set of recursively enumerable languages ($emptyset subsetneq C subsetneq mathrm{RE}$) and let $L$ be the set of encodings of Turing machines that recognize some language in $C$: $$L={langle M rangle mid L(M) in C Read More …
[Solved]: Precise definition of term: *schema*
Problem Detail: Does the term schema, in the context of describing a structure, refer to the actual structure of the data, or the description of this structure? I.e. can I talk about the schema of an entity without a schema language? Read More …
[Solved]: Hardness proof of EVEN-ODD PARTITION
Problem Detail: The PARTITION problem is NP-complete: INSTANCE: finite set $A$ and a size $s(a) in mathbb{Z}^+$ for each $a in A$ QUESTION: Is there a subset $A’ subseteq A$ such that $sum_{a in A’} s(a) = sum_{a in A setminus Read More …
[Solved]: Null Hypothesis in Analysis and Testing
Problem Detail: I have my end of year exams next Thursday. I’m generally doing fine but I am having some major issues with this strand of my course, this has to be the biggest issue I have. So, here is the Read More …
[Solved]: What do I need to study in order to understand and design a programming language?
Problem Detail: What do I need to read in in order to : understand the specs of an already made programming language Design a programming language Design a compiler and assembler for that language make an architecture of a processor Asked Read More …
[Solved]: Can we compute the sum of a range of entries in $O(1)$ time?
Problem Detail: I have encountered a few tests in algorithms which ask for a data structure which allows to get the sum of all the elements of an array in the range [i..j], in O(1) time. Is it even possible to Read More …
[Solved]: Show that the pumping lemmas for context-free and regular languages are equivalent for unary languages
Problem Detail: I want to show that for any language $L subseteq { a }^* $, $L$ satisfies the pumping lemma for context free languages if and only if it satisfies the pumping lemma for regular languages. I know that every Read More …
[Solved]: Understanding a proof in the sweep line algorithm when finding all line segment intersections
Problem Detail: You have a set of line segments and you want to find all intersections. First sweep line approach: Use a priority queue Q for the events as they come, where each event is just an end point of a Read More …
