Question

For each of the following languages, use JFLAP to draw the state diagram of a deterministic finite automaton (DFA) that accepts the

language.
a) 1 = { ∈ {0,1}∗| starts with a 1 and its number of Os is a multiple of three}
b) 2 = { ∈ {0, 1}∗| in which every 1 is either immediately preceded or immediately followed by 0. such as 0110, 101, 0}
c) 3 = { ∈ {0,1}∗| does not start with 110}
d) 4 = { ∈ {0,1}∗| in which substring 11 occurs at least twice}

Answer 1

The provided outlines describe how to create state diagrams for DFA accepting four specific languages, with each requiring unique state transitions to ensure that the language's particular conditions are satisfied.

Step-by-step explanation:

Creating state diagrams for deterministic finite automata (DFA) requires understanding the specific language requirements for each automaton. Below are the outlines for creating DFA state diagrams for the given languages:

• Language 1 (starts with a 1 and its number of 0s is a multiple of three): Begin with a start state that transitions to an accept state with input 1. Create additional states to keep track of the count of 0s mod 3 to ensure only multiples of three 0s lead to accept states.
• Language 2 (every 1 is immediately preceded or followed by 0): From the start state, transition to a non-accept state with input 1, which goes to an accept state with 0, and loop back on 0 input. Additionally, create transitions from the start and each state to handle the immediately preceding condition.
• Language 3 (does not start with 110): Create a series of states that attempt to track the '110' prefix, making sure none of those leads to an accept state. All other combinations should lead to an accept state.
• Language 4 (substring 11 occurs at least twice): Construct states that track occurrences of adjacent 1s, transitioning to an accept state after the second occurrence is detected and maintaining that acceptance with any further inputs.

Each language imposes unique conditions on the accepted strings, and as such, each DFA will be structured to ensure those conditions are met. These explanations provide a general guideline, and the actual implementation requires careful state management within the context of JFLAP.