(a) Show that L requires a DFA with at least 2k states. (b) Show that an NFA for L exist with only k + 1 states.
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Question: (a) Show that L requires a DFA with at least 2k states. (b) Show that an NFA for L exist with only k + 1 states. Step-by-Step Solution: (a) Show that L requires a DFA with at least 2k states. ** Show more…
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Show that if L is a nonempty language such that any w in L has length at least n, then any DFA accepting L must have at least n+1 states. (Suggestion: Use proof by contradiction method).
Adi S.
(a) The size of the DFA corresponding to M1 is 2. (b) The size of the DFA corresponding to M2 is 5. (c) The size of the DFA corresponding to M3 is at least 9. Consider the incomplete NFA M0 below, whose alphabet is {0, 1}. Use M0 to create three more NFAs M1, M2 and M3 according to the constraints below. Explain in one or two English sentences how you constructed each NFA. Each of M1, M2 and M3 must contain at least 10 transitions (potentially but not necessarily including λ-transitions) and must be an NFA but not a DFA. Specifically there must be at least one combination of state and input (either 0 or 1) for which there are at least two possible states. Put another way, removing all λ-transitions must not result in a DFA. Use JFLAP to transform M1, M2 and M3 into equivalent DFAs. The sizes of the DFA resulting from the determinising algorithm must be as below. Note that the JFLAP implementation of this often omits an "error" state, i.e. it may be necessary to add an extra state to the result from JFLAP in order to account for this. The size constraints below assume a fully deterministic DFA; one way to check for this is that if the DFA has k states, there must be exactly 2k transitions (one for each of 0 and 1 in each state).
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What is the minimum number of states required in any dfa to accept the regular language l= {all binary strings that starts and ends with the same symbol}? a, 3 b,4 c, 5 d, 6
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