- Solve $\min_{\mathbf{x},\mathbf{R},\mathbf{\lambda}}\left\|\mathbf{y}-\mathbf{x}\right\|_{\mathbf{R}}^2+\mathbf{\lambda}^T\mathbf{A}\mathbf{
- Rudin theorem 5.19, MVT for vector function
- On the Definition of the Derivative
- Convergence both in $L^p$ and $L^q$
- Polynomial cannot have all roots real?
- How do I find the set of functions that would make this non-linear operator diverge?
- If $X$ has more than one element, then the norm $||f||=\sup_{x\in X}|f(x)|$ don't come from a inner product
- $X$ and $Y$ independent and uniform on $[0,1]$. Find PDF of $X+Y$.
- Find the Dimension of the Centraliser of Matrix $A$
- Asymptotic rate of the largest order statistic.
- Finding the value of largest integer among a set given multiplicative and additive constraints
- Linear Transformation of a Polynomial
- Show that for each number $n > 0$, $nx^{1/n} < ln(x)$ for $x > 1$
- Epimorphism and monomorphism explained without math?
- How do you use the predictive distribution with noise in Bayesian Optimization?
- Longitudinal panel data classification
- Algorithm for selecting largest possible value, when observing online sequence of unknown distribution?
- Combination question with and without replacement
- Cox PH linearity assumption: reading martingal residual plots
- At a loss regarding feature selection vs coefficient estimation. Can you ever re-do the latter after the former?

# Are addition expressions a regular language?

For an alphabet $\Sigma = \{1, +, =\}$ and language

$L= \{ 1^m

+1^n

=1^{m+n} | m, n ∈ \mathbb{N} \}$, is $L$ regular?

So here are my thoughts: I do not believe this language is regular. This is because I cannot conceive of designing a regular expression, DFA, or NFA for it. There is simply no finite way to keep track of how many $1$'s are in each location relative to $=$ and $+$. However, Myhill-Nerode does not seem to work, as every string in $L$ is a "balanced" equation and adding any number of $1$'s to a string in $L$ would make it no longer a member of $L$. Now, using Myhill-Nerode (and not the Pumping Lemma or any other tools), is there a way to prove that $L$ is regular? Alternatively, if $L$ is actually not regular, I would greatly appreciate any hints as to how to go about designing a regular expression for $L$.