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We now add an additional degree of non-determinism and allow transitions that can be taken independent of the input-ε-transitions.
Here whenever the automaton is in state 1 it may make a transition to state 3 without consuming any input. Similarly, if it is in state 0 it may make such a transition to state 2. The advantage of such transitions is that they allow one to build NFAs in pieces, with each piece handling some portion of the language, and then splice the pieces together to form an automaton handling the entire language. To accommodate these transitions we need to modify the type of the transition relation to allow edges labeled ε.
In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
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A common approach in solving problems is to transform them to different problems, solve the new ones, and derive the solutions for the original problems from those for the new ones
All that distinguishes the de?nition of the class of Regular languages from that of the class of Star-Free languages is that the former is closed under Kleene closure while the lat
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The k-local Myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languages. Lemma (k-Local Suffix Substitution Clo
Let G be a graph with n > 2 vertices with (n2 - 3n + 4)/2 edges. Prove that G is connected.
Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
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