0
votes
2answers
72 views

Show that, given regular expression $R$, we can decide whether $L(R)$ is prefix-free

Suppose language $L$ is called prefix-free if no member is a proper prefix of another. For instance, cat is a proper prefix of category and so $L = \{cat,category,ego,go,rye\}$ is not prefix free. ...
1
vote
1answer
22 views

Showing that all regular languages are closed under reversal

I'm trying to show that $L^{reverse} = \{w^{reverse}:w \in L\}$ is a regular language. The first argument I can come up with is simply: if we have an NFA for $L$, then an NFA for $L^{reverse}$ can be ...
0
votes
1answer
31 views

Help Specify possible definitions for this Boolean Function

My math is rusty, but I need some guidance here. Problem I wish to design a stochastic, boolean procedure $f(state)$, that picks a winner, $f(state_{win})\to 1$ or loser, $f(state_{loss})\to 0$. I ...
2
votes
2answers
221 views

Regular Languages Algorithm?

I need help proving the following question: Let $L$ be any regular language on $\sum{a,b}$. Show that an algorithm exists for determining if L contains any strings of even length. So far, I know ...
1
vote
1answer
303 views

How to prove CYK algorithm has $O(n^3)$ running time

I have a final coming up in few days, and the professor mentioned the CYK algorithm. I want to be prepared for the final. I'm trying to find out how to prove the algorithm has worst case running time ...
7
votes
2answers
193 views

Density of black cells in rule 110

Is there a way to compute the limit of the ratio (number of black cells)/(number of white cells), in the rule 110 or rule 30 automaton? With initial state = 1 black cell. Simulation of first 120000 ...
3
votes
2answers
403 views

Help in constructing a DFA equivalent to this NFA

First post here, woot. I've been a member of Stack Overflow for a while, so hopefully you guys are just as friendly! I'm having issues converting simple NFAs to DFAs... I just don't get it. ...
0
votes
2answers
398 views

String matching automata preprocessing

I have an alphabet A = {a,b,c} and a pattern P = "abcaab". The task is to build a finite automaton of the transition function (delta) for {0,6} (the length of the pattern) and each element of the ...
2
votes
1answer
200 views

Generating all words in a language from CFG

I have a non-ambiguous context-free grammar. Is there some standard algorithm to create list of all the words in the language the CFG defines? This can be done with an abvious brute-force search by ...