Deterministic Omega Automata

Question

An automata is deterministic if it is designed as per below conditions :

1. Only 1 initial state in entire automata.

2. From one state on a unique input should make a transition to another state.

3. Should have transition from all combination of inputs (set of inputs)

Could you please confirm if above description is correct regarding the deterministic automata ?

If there is something else I am missing could you please let me know ?

Answer 1

An automaton is deterministic iff it has only one initial state and the transition relation is a total function from inputs and states to states. Hence, every word has a unique run. That is all that you need.

Comments

Thank you for this explanation.