4 votes 4 votes The number of possible finite automata with two states $a0$ and $a1$ (where $a0$ is always the initial state over the alphabet $\{p, q\}$) which accepts empty language is _______ . Theory of Computation tbb-toc-2 numerical-answers theory-of-computation finite-automata + – Bikram asked Aug 12, 2017 retagged Sep 17, 2020 by ajaysoni1924 Bikram 602 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments tarGATE commented Nov 25, 2017 reply Follow Share This will help you 3 votes 3 votes bhuv commented Jan 12, 2018 reply Follow Share Those who are wondering about this pic and scratching head how 20? First of all, there is a0 where 2 combination possible either p loops on a0 or goto a1, similarly we have choices of q on a0 either to loop or goto a1 and forwarding that logic to a1 also we in total (2*2*2*2) 16 such combinations. **take your time to get these lines first, try to draw 1 or 2 combinations, you'll get them." Now, we got to choose the final and non-final state and final state, which gives us 4 combinations, now read the question the last line "accepts empty language", 3rd and 4th Combinations is accepting more than "empty means nothing"i.e at least they are accepting $\lambda$ so, they are out. No, combination-1 is clearly an empty language accepting FA as there is no accepting state so, 16 are these combinations. Going towards combination-2, which is further explored below, out of 16 only 4 are shown which are favorable to accept "empty language" (4 comes from here). So total 16+4=20 2 votes 2 votes jugnu1337 commented Apr 24, 2022 reply Follow Share @Arjun sirplease give proper solution 0 votes 0 votes Please log in or register to add a comment.