Any answer that involves a design for a Finite Automaton (DFA) should contain information about the following five components of the FA (corresponding to the 5-tuple description): i) The set of states Q; ii) the alphabet Σ; iii) the start state; iv) the set of final states F; v) the set of transitions δ, which can be either shown in the form of a state diagram (preferred) or a transition table. You can either present the answer in the form of a state diagram with all the above information (as shown in the left side of slide #8 in the Finite Automata lecture notes) or in the tabulated form (as shown in the right side of the same slide). State diagram representation is preferred. 1. Give a DFA for each of the following languages defined over the alphabet Σ = {0, 1}: a) L={ w | w contains the substring 101 } b) L={ w | w ends in 001 } c) L={ w | w has a 1 in its 2nd last position, if such a position exists}
Any answer that involves a design for a Finite Automaton (DFA) should contain
information about the following five components of the FA (corresponding to the 5-tuple
description):
i) The set of states Q; ii) the alphabet Σ; iii) the start state; iv) the set of final states F; v) the set of transitions δ, which can be either shown in the form of a state diagram (preferred) or a transition table. You can either present the answer in the form of a state diagram with all the above information (as shown in the left side of slide #8 in the Finite Automata lecture notes) or in the tabulated form (as shown in the right side of the same slide). State diagram representation is preferred.
1. Give a DFA for each of the following languages defined over the alphabet Σ = {0, 1}:
a) L={ w | w contains the substring 101 }
b) L={ w | w ends in 001 }
c) L={ w | w has a 1 in its 2nd last position, if such a position exists}
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