computability – Prove if $L = {0^m1^n mid m neq n}$ is regular or not

I am trying to show whether this language is regular or not:

$$L = {0^m1^n mid m neq n}$$

Since I cannot create or think of an automaton that recognizes $L$, I am suspecting that $L$ is not regular. From the book I am using, it seems I can use the pumping lemma, I have done this:

Let $p$ be the pumping lemma constant, and let $w=0^p1^{p+1}$

In this case
$$|w|=2p + 1geq p$$

We can divide $w$ into $xyz$, where $x=0^{p-1}$, $y=0$, $z=^{p+1}$, then $|y|geq 1$

If L was regular, then $forall k geq 0, xy^kz in L$. Let choose $k=2$, then:


Here is where I am stuck, how do I prove that $L$ is not regular?

Another question, pumping lemma applies only to infinite languages?

All string matches for regular expression

Given a regular expression, the ask is to find all matches in a string, str.
Most implementations give longest match only. For example, [a]* in str “aaaaaa”, the regex libraries in C++ or python only provide the longest match, i.e. { “aaaaaa”, “” } at position 0 and 6 respectively.
How can one obtain all matches like { “” , “a”, “aa”, “aaa”, “aaaa”, “aaaaa”, “aaaaaa”} with C++ regex libraries.

Convert finite automata to regular expression

I am trying find the regular expression that describes the finite automata in the image below.

Given the following finite automata Finite Automata

which of the following regular expressions describes the same language as the automaton.

  • (ab)+c*d+
  • a+b+c*d+
  • a(ba)*bc*dd*
  • (ab)+c*d+
  • a(ba)*bc+d?d+
  • (ab)+c+d*

I tried converting it to a regular expression and I got (ab)*ac*dd*, which is not among any of the options. Could someone help me select the correct answers?

finite automata – Regular language is closed given transposition of rightmost character to leftmost

This answer assumes that the transposed language never contains the empty string.

Let $L$ be a regular language, say accepted by a DFA with states $Q$, initial state $q_0$, accepting states $F$, and transition function $delta$.

We construct a new DFA with states $Q’ = q’_0 cup (Q times Sigma)$. The initial state of the new DFA is $q’_0$. The transition function is defined as follows: $delta'(q’_0,sigma) = (q_0,sigma)$, and $delta'((q,sigma),tau) = (delta(q,tau),sigma)$. Finally, the set of accepting states $F’$ contains all states $(q,sigma)$ such that $delta(q,sigma) in F$.

The new DFA reads the first symbol $sigma$ and remembers it. It then simulates the original DFA, accepting a word if adding $sigma$ would result in the original DFA accepting it.

php – Change Sale Price to Regular Price WooCommerce

I have imported some products from CSV but made a mistake, set the Regular Price as Sale Price.

Now as the Regular Price of the products are not et, so no price is showing on the product.

So, is there a code or plugin available so that I can remove the Sale Price at once and add that value to the Regular Price area?

Looking forward to some help.

Thank you.

formal languages – Check if given safety properties are regular, and if so construct NFAs

Let $mathit{AP} = {a, b, c}$. Consider the following LT properties:

  1. Between two neighboring occurrences of $a$, $b$ always holds.
  2. Between two neighboring occurrences of $a$, $b$ occurs more often than $c$.

For each of these properties $P_i$ (where $1 leq i leq 2$), decide if it is a regular safety property (justify your answers) and if so, define the NFA $A_i$ with $L(A_i) = mathrm{BadPref}(P_i)$.

How to keep a custom map visible during a regular google maps search?

I have a custom map saved. On the computer, I view it by going to [Hamburger Icon] > Your places > Maps. When I click on the map, I can see the places on that map. But I want to search hotels near some of those places, and I can’t figure out how. When I hit the back arrow, the map disappears. How can I keep my custom map visible during a normal Goole maps search? Surely this has to be possible…

How to show that this language is not regular with pumping lemma?

Being L={a^x b^y c^z: x=2y ∨ y>z I have to prove that this language is not regular, making use of the Pummping Lemma, I know that for that, I have to assume that L is regular, then I know that there is a p such that every w in L such that |w| >= p can be represented as x and z with |y| != 0 and |xy| <= p. But I have not been able to choose a w in L that serves me to finish with the lemma, taking into account the restrictions that L has.