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## How to prove this language is not regular?

I am currently learning Pumping Lemma and found this question. But I am not able to prove it not regular. L = { $$0^n$$ | n is power of 2}. So, here I considered w = $$0^{2^n}$$ where n is constant of Pumping Lemma. Then divided w into xyz where y $$\ne \epsilon$$ and |xy| $$\leq$$ n. Hence, |y| will be between 1 and n. So, |x$$y^k$$z| satisfies L if |y| = 2 for all values of k and it is within the bound. So, how is L irregular? The question is to prove it is irregular but here it is coming as regular.

## Strongly connected components in a regular directed graph

Hello guys i have a quit question.

Let G be an arbitrary directed graph. Does G always have the same strongly connected components on G as on G*? G* is the inverted Graph of G (if (u,v) e E -> (v,u) e E*) I’m thinking yes because otherwise the algorithm of Kosaraju would not work at all? But do not have another explanation for this.

## Is there a language that pumps, but is not regular?

I’m looking for a concrete language that can be pumped but is not regular. I understand that closure properties can be used to further test if a language is regular/nonregular.

## A deterministic finite state automata for finding all (potentially overlapping) regular expression matches?

I was working on a bioinformatics practice problem named Finding a Protein Motif on rosalind.info. In essence, I was given a particular regular expression N[^P](S|T)[^P] and is asked to find all matches.

Solving that problem is not the goal here, I have a ‘working’ solution here. In essence, I manually designed a state machine that can find all matches for that regular expression.

And here is a ‘visualization’ of the state machine, to make it clear how it is manually designed.

digraph G {     0 [label="0,''"]     1 [label="1,'N'"]     2 [label="2,'NN'"]     3 [label="3,'NS|NX'"]     4 [label="4,'NNS'"]     5 [label="5,'NSS|NXS'"]     0 -> 1 [label="N"]     0 -> 0 [label="P"]     0 -> 0 [label="S"]     0 -> 0 [label="X"]     1 -> 2 [label="N"]     1 -> 0 [label="P"]     1 -> 3 [label="S"]     1 -> 3 [label="X"]     2 -> 2 [label="N"]     2 -> 0 [label="P"]     2 -> 4 [label="S"]     2 -> 3 [label="X"]     3 -> 1 [label="N"]     3 -> 0 [label="P"]     3 -> 5 [label="S"]     3 -> 0 [label="X"]     4 -> 1 [label="N(accept)"]     4 -> 0 [label="P"]     4 -> 5 [label="S(accept)"]     4 -> 0 [label="X(accept)"]     5 -> 1 [label="N(accept)"]     5 -> 0 [label="P"]     5 -> 0 [label="S(accept)"]     5 -> 0 [label="X(accept)"] } 

The classical theory allows us to convert a regular expression to a non-deterministic finite-state automaton and then convert it to a deterministic finite-state automaton through subset construction. In particular, subset construction guarantees that if there exists an accepting computation, then the deterministic finite-state automaton would also accept.

Let say I have a regular expression that matched twice, the corresponding deterministic finite-state automaton would accept after the first match, but then it doesn’t know what to do in order to set it to the right state for detecting overlapping matches. I guess I could start one character after the beginning of the first match, which in the worst case would probably lead to quadratic time, as we could imagine with {.*} on {{{{{}

In the worst case, I expect quadratic time (e.g. {{{{{}}}}}}), but it would be great if the timing is output-sensitive, for I believe a good deal of cases aren’t quadratic in output size.

It would be great if my state machine used to find all matches can be generalized (apparently sometimes it need linear space, not just a single state) or automatically designed. Do we know if there are existing theories for that?

## Add Regular Expressions with grep

I have to use grep to find 8 postcodes out of a text file, the order of characters of each postcode is as follows: 1. Capital letter 2. Digit 3. Capital letter 4. Space (optional) 5. Digit 6. Capital Letter 7. Digit

I have used the grep command:

grep '[A-Z][0-9][A-Z][0-9+[][0-9][A-Z][0-9]' 

This has given me 5 postcodes which have a space at character 4

I have also used this grep command:

grep '[A-Z][0-9][A-Z][0-9\.][A-Z][0-9]' 

This has given me the last 3 postcodes with no space at character 4.

I don’t know how to write a command that states that a space can be optional. Thanks

## negar expresion regular en r

me encuentro con el siguiente problema. De la siguiente columna, quiero obtener solo los dígitos o composición de ellos, esto es, números o numero-numero: ejemplo 3,4,6 o 20-30

transprods <- data.frame(producto = c("tipo1 marca1 azul 22-33",                                   "tipo2 marca2 az 10/20",                                   "tipo3 marca2 rojo 30",                                   "tipo4 marca21 amarillo am 20",                                   "tipo1 marca3 am 20/10 cac",                                   "tipo3 marca2 lila 15/25",                                   "tipo2 marca2 30 3 azul",                                   "tipo1 marca3 30/20 amarillo")) %>% as.tibble 

cuya salida es:

  producto                     <fct>                        tipo1 marca1 azul 22-33      tipo2 marca2 az 10/20        tipo3 marca2 rojo 30         tipo4 marca21 amarillo am 20 tipo1 marca3 am 20/10 cac    tipo3 marca2 lila 15/25      tipo2 marca2 30 3 azul       tipo1 marca3 30/20 amarillo  

lo que primero hago es normalizar los numero con “/” para que sean separados por un “-“

luego, aplico la expresion regular

productos %>% mutate(producto = gsub('[/]','-',producto),      X2 = gsub('([0-9]+[-][0-9]+|\d{2})','',producto))  A tibble: 8 x 2 producto                     X2                         <chr>                        <chr>                      tipo1 marca1 azul 22-33      "tipo1 marca1 azul "       tipo2 marca2 az 10-20        "tipo2 marca2 az "         tipo3 marca2 rojo 30         "tipo3 marca2 rojo "       tipo4 marca21 amarillo am 20 "tipo4 marca amarillo am " tipo1 marca3 am 20-10 cac     tipo1 marca3 am  cac       tipo3 marca2 lila 15-25       "tipo3 marca2 lila "       tipo2 marca2 30 3 azul        tipo2 marca2  3 azul       tipo1 marca3 30-20 amarillo   tipo1 marca3  amarillo  

que elimina todos los números y numeros separados con “-” pero cuando quiero negar la expresión mediante el patrón '^([0-9]+[-][0-9]+|\d{2})' para quedarme solamente números y numeros separados con “-” queda la misma columna del inicio.

Cómo se debe aplicar correctamente la negación ^ o ?! ? lo intente con ^[[0-9]+[-][0-9]+|\d{2}], ^([0-9]+[-][0-9]+|\d{2}), ?![[0-9]+[-][0-9]+|\d{2}], ?!([0-9]+[-][0-9]+|\d{2})

sin ningún resultado satisfactorio, cómo debería aplicar correctamente la negación? Agradezco desde ya su ayuda

## Regular Expression: Writing an expression with at least two characters in length?

A past exam question: (1) Consider the language, L, of strings over the alphabet {x, y} of length at least 2 with the second symbol being x. For example, yx, xxyy, and yxy are members of L while xy, yyy,and yyxx are not in L.

(a) Write a regular expression to describe the language L.

I thought perhaps EXE* would be the correct answer, but then E could be either an empty string or X or Y, and the empty string would make it no longer valid because X wouldn’t be the second symbol. Is there some kind of statement that could (x + y)XE*?

## Is it unsafe to enter administrative Windows credentials when logged in as a regular user?

I was recently advised that when a user is logged in as a regular user and they need an administrator to do something (i.e. install an application) that entering the administrator credentials when the regular logged in user is still logged in, puts the credentials at great risk and logging out as the regular user and logging in as the administrator is the recommended course of action. Is this correct?

## Is finite subset of a set which contains all non regular languages a regular set?

Let A be a set which contains all non-regular languages. Then set B which is finite subset of A. Then will it be regular ?

I know that A is not recursive enumerable set (undecidable). So I wonder that if finite subset of undecidable set is a regular language or not.