Intereting Posts

On the properties of the Sobolev Spaces $H^s$
(weak) homotopy equivalence
Pattern finding for repeating sequences
Triangle forming probability for area
Solve $y'-\int_0^xy(t)dt=2$
Equivalent limit definition
Difference between the Jacobian matrix and the metric tensor
Can a function be increasing *at a point*?
If a group is the union of two subgroups, is one subgroup the group itself?
Prove that $\sum\limits_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$?
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
Substitution for bound variables in logic
How do we describe the equivalence between $f:(I,\partial I)\to(X,x_0)$ and its “naturally equivalent” map $\tilde f:(S^1, s_0)\to (X,x_0)$
How to prove a set equality?
Manifold Boundary versus Topological Boundary.

Draw a finite state machine which will accept the regular expression:

$(a^2)^* + (b^3)^*$

In particular, I am confused by the $+$ sign, what does it exactly mean? Most literature I could find about $+$ is $a^+$, which means 1 or more $a$; but here it is clearly not the same meaning.

- NFA from grammar productions
- Converting from NFA to a regular expression.
- Difference between NFA and DFA
- Greibach normal form conversion
- Proving that the language $\mathscr L$ is non regular using the pumping lemma
- Can you draw the e-NFA from the following definition?

- Using Direct Proof. $1+2+3+\ldots+n = \frac{n(n + 1)}{2}$
- If a plane is divided by $n$ lines, then it is possible to color the regions formed with only two colors.
- Compute the following sum $ \sum_{i=0}^{n} \binom{n}{i}(i+1)^{i-1}(n - i + 1) ^ {n - i - 1}$?
- Complex Permutation
- Counting non-isomorphic relations
- Why is this relation $R=\{(a,b), (b,c), (c,a)\}$ transitive?
- How to find a function that is the upper bound of this sum?
- Time to reach a final state in a random dynamical system (answer known, proof unknown)
- Rubik's cube and counting
- How many possibilities to arrange a rope of length $N$ between two points

Start at state $q_{0}$. On input of $a$, transition to state $q_{1}$. On input of $b$, go to $q_{2}$.

While on $q_{1}$, if there is an input of $a$, go to $q_{0}$.

While on $q_{2}$, if an input of $b$, go to $q_{3}$. On $q_{3}$, on input of $b$, go to $q_{4}$. While on $q_{4}$, go to $q_{2}$ on input of $b$.

The accepting states are $q_{0}$ and $q_{4}$. Of course, you could have $q_{0}$ and $q_{4}$ go to a separate accepting state on input $\epsilon$, the empty string.

Here is the drawing:

The idea is that the machine has two counters, one for `a`

s and one for `b`

s, indicated by the orange boxes. Since it accepts *either* a number of `a`

s that is a multiple of 2, *or* a number of `b`

s that is a multiple of 3, it only needs to choose which of these counters to use. Upon seeing the first symbol in the input, either `a`

or `b`

, it chooses which of the counters to use, and thereafter circulates around the counter. One state of each counter is an accepting state. If the wrong symbol appears while the machine is counting, it goes into ‘dead’ state $x$, from which it cannot escape; transitions to state $x$ are drawn in red.

I’m guessing it’s similar to the notation used in this post on CS, where the author uses it to mean OR.

Applying to your example, your FSM must accept an even number of `a`

s, or a number of `b`

s divisible by three.

So, to draw the graph, first draw the graph for $(a^2)^*$. Then, draw the graph for $(b^3)^*$. Then, put a start state, say $s$, and transitions consuming the empty string from $s$ to the two graphs.

- Inclusion of Fields whose order is a prime power
- A formal name for “smallest” and “largest” partition
- If $\int_0^\infty {e^{-\lambda t}f(t){\rm d}t} = 0$ for all $\lambda >0$ then $f=0$ a.e.?
- Is a decimal with a predictable pattern a rational number?
- The cone is not immersed in $\mathbb{R}^3$
- Equivalent characterisations of Dedekind-finite proof
- About finding $2\times 2$ matrices that are their own inverses
- How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it?
- Probability that a vector in $\mathbb{Z}^n$ is primitive
- Variation under constraint
- Valuations, Isomorphism, Local ring
- Discontinuous function at an uncountable set with not rationals
- Real world uses of Quaternions?
- Show that $\tan 3x =\frac{ \sin x + \sin 3x+ \sin 5x }{\cos x + \cos 3x + \cos 5x}$
- Spivak's Calculus – Chapter 1 Question 1.3