Cardinal Path’s response to COVID-19 Cardinal Path is sharing all we know to help marketers during COVID-19.  Learn more.

Original posted on Erik Vold’s Blog

The Problem:

For the regular language L = { w | w mod 3 = 0 }, where the alphabet is {0,1,2,3,4,5,6,7,8,9}; give the deterministic finite automaton (DFA) for L, and convert this to a regular expression.

The Solution:

The DFA ( S, Σ, T, s, A ):
S = {q0,q1,q2}
Σ = {0,1,2,3,4,5,6,7,8,9}
T = (doing the state diagram below)
s = {q0}
A = {q0}

For shorthand I will divide the alphabet, Σ, into:

  • A={0,3,6,9}
  • B={1,4,7}
  • C={2,5,8}

Now to convert the DFA state diagram into a regular expression. This is done by converting the DFA into generalized non deterministic finite automaton (GNFA), and then converting the GNFA into a regular expression.

Notice in the above that I did two steps in one; I first converted the DFA into a GNFA (which is the easy part), then I removed the q0 state.

Removing the q1 state:

Finally, removing the q2 state

Therefore the regular expression that defines the regular language L is:

For further reading please see “Introduction to the Theory of Computation” by Michael Sipser


State of Digital Marketing Analytics

The 2020 State of Digital Marketing Analytics examines the marketing technology that supports the world's most successful enterprises and highlights the challenges and strategies for navigating the new normal..