Final answer:
Constructing a DFA for languages that are not (10+110)* involves creating a DFA that accepts (10+110)*, then swapping the accept and reject states and ensuring the resulting DFA is complete with appropriate transitions.
Step-by-step explanation:
The question asks to draw the state diagram of a DFA (Deterministic Finite Automaton) that accepts all binary words that are not in the language defined by the regular expression (10+110)*. This task requires understanding of automata theory, which is part of theoretical computer science, and designing a DFA that recognizes the complement of the specified language.
To create a DFA rejecting (10+110)*, you start by constructing a DFA for (10+110)*, then you make the accepting states non-accepting and the non-accepting states accepting. In the DFA for (10+110)*, the string '10' or '110' can repeat any number of times including zero. The state diagram for this has a start state that loops back to itself on '1', transitions to an accept state on '10', and then goes back to the start; there's also a transition from the start to an intermediate state on '1', then to the accept state on '10', and back to the start.
For the complement, every state that was accepting in the original DFA becomes a reject state and vice versa. Additionally, we must ensure that the modified DFA is complete, meaning it has a transition for each symbol in every state. States that would lead to acceptance in the original DFA should now lead to a trap state from which there is no escape, thus ensuring rejection of strings in (10+110)*.