![]() Advantage of $$ya$$ is that we can use different parts of it to define $$δ^∗(q, ya)$$. $$ya$$ in $$δ^∗(q, ya)$$ means, concatenationīetween a string $$y$$ from $$Σ^*$$ and one symbol $$a$$ from the alphabet $$Σ$$. Recursive case defines function for those cases when a string is not empty. Just like $$δ$$ transition would return the state after last input symbol. Empty string $$ε$$ indicates the end of the string, so it makes sense to return It may sound useless but in fact, it is very important case because, as we In plain english, function $$δ^∗$$ says: give me any state and empty string and We start with the base case which says thatįor every $$q ∈ Q$$, $$δ^∗(q, ε) = q$$. So Kleene closure is a nice way of representing all those strings.Īfter defining $$δ^∗$$ signature, we need to define how it functions. You may ask: why do wee need it? Remember, automaton accepts strings where each symbol is in alphabet $$Σ$$. It represents all the symbols which are allowed to go into machine.įor example, if $$Σ = \$$ Second element is an alphabet $$Σ$$ (read as sigma). In general, when we are talking about finite state machine, term finite state is analogous to $$Q$$. First element $$Q$$ represents all the states
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