Problem Detail: I have my own version of lex and I would like to add the complement operation. Derived from that I can then add the intersection and difference also. My version also supports the generation of NFAs (Non-deterministic Finite Automaton) Read More …
Author: ignougroup
[Solved]: What is a fixed point in the context of Roger’s fixed-point theorem?
Problem Detail: In the Wikipedia article on Rogers’ theorem, it is stated that all total computable functions have a fixed point. The notation is a little hard for me to understand; a symbol is used that is used to denote “semantic Read More …
[Solved]: What does it mean to say that there doesn’t exist an algorithm from a TM point of view?
Problem Detail: A TM for a recursive language corresponds to our informal notion of an algorithm. as per Automata Theory, Languages and Computation by Ullman et al. Then there are languages called RE and $L_d$, where there exist TM that Read More …
[Solved]: Modification of Hamilton Path
Problem Detail: Although I know that the Hamilton Path problem is ${sf NP}$-complete, I think the following variant can be solved in polynomial time: Given a planar graph with vertex set $V$, edge set $E$, start node $S$ and target node Read More …
[Solved]: Equality testing of arrays and integers in a procedural language
Problem Detail: In terms of references and their implementation on the heap and the stack, how is equality testing for arrays different from that for integers? This is to do with Java programming, if you have a stack and a heap, Read More …
[Solved]: About Codd’s reduction algorithm
Problem Detail: Codd’s Algorithm converts an expression in tuple relational calculus to Relational Algebra. Is there a standard implementation of the algorithm? Is this algorithm used anywhere? (It seems that the industry only needs SQL and variants, I’m not sure about Read More …
[Solved]: Complexity classes that are closed under subtraction
Problem Detail: Are NP or P closed under subtraction? Im having a hard time deciding whether they are or aren’t. Question was edited Original question: Im having some hard time figuring out what languages are closed under subtraction. Say you have Read More …
[Solved]: 3 Colorability reduction to SAT
Problem Detail: I’d like to reduce 3 colorability to SAT. I’ve stuffed up somewhere because I’ve shown it’s equivalent to 2 SAT. Given some graph $G = (V,E)$ and three colors, red, blue, green. For every vertex $i$, let the boolean Read More …
[Solved]: What is it called when two problems are similar?
Problem Detail: Suppose that there are two problems $P$ and $Q$. How can I say that “solving $P$ is same thing with solving $Q$”? For instance, if $P$ is NP-Hard, then we can say “$P$ can be solved in polynomial time Read More …
[Solved]: Confusion about the Time Hierarchy Theorem and relativization
Problem Detail: I know that $mathsf{P}^A = mathsf{EXP}$ for any $mathsf{EXPTIME}$-complete language $A$. Is it true that $mathsf{DTIME}^A(n^k) = mathsf{EXP}$ for any fixed $k$ and any $mathsf{EXPTIME}$-complete oracle $A$? If not, what do these complexity classes equal and why? I am Read More …
