Question

A Discrete mathematics question shows on the image, could you please show the detailed procedures, thank you!

Given the following deterministic FSM M over the alphabet Σ- (0,13: 1 S1 S2 1 1 S3 (a) Give an English language description of L(M), the language recognised by M. (b) Add an error state (labelled X) to the diagram, and draw all transitions to it (c) Describe how to derive an FSM that accepts the complement of L(M) over the set . (That is, an FSM that accepts the language - L(M).) (d) Give a regular expression for the complement of L(M)

Answer 1

Given FSM is the following diagram. - Ô Here, &- $0,1]. & 8={s,,S2, 33} b F={5,,S2,S3} b s, is starting state. (a) from the diagram we can see that it accepts call the string if number of o's in the string is <3. las all states are final state of more than two o's goes to dead Stone ) L(M) 2 { WEE* l w contains less than 3 os } the, Lims=4 Well I Wola 38 [Wo is number of o's in will (6) let x be an error state. Then the FSM will be (c) To find the FSM accepting complement of L(m) is consider, the FSM (E,Q,S,S, ,F) where only change is in Q = qs,,S2 , B 3 , X} and F = {x}. and s is defined on in lbs. So, language accepting is = { WEE* l I wo 17,37 = &- Lom) proved)