(a) Consider the following Deterministic Finite Automaton (DFA): 0 90 91 93 92 0,1 (i) State...

 

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(a) Consider the following Deterministic Finite Automaton (DFA): 0 90 91 93 92 0,1 (i) State which of the following groups of words would be recognised by the automaton: Group 1 Group 2 10 01 010 011 101 0111 (ii) Give a set definition for the language of this automaton. (iii) Give a formal, 5-tuple, definition of the DFA. [2 marks] [5 marks] [8 marks] (b) The most simple arithmetic expressions of multiplication take the following form: a digit (d) is followed by the operator (+), followed by another digit d, and possibly followed by the operator and another digit etc. For example the strings d+d, d+d+d, d+d+d+d etc. are all valid expressions. Design a DFA which accepts strings which form valid expressions. [5 marks] (a) Consider the following Deterministic Finite Automaton (DFA): 0 90 91 93 92 0,1 (i) State which of the following groups of words would be recognised by the automaton: Group 1 Group 2 10 01 010 011 101 0111 (ii) Give a set definition for the language of this automaton. (iii) Give a formal, 5-tuple, definition of the DFA. [2 marks] [5 marks] [8 marks] (b) The most simple arithmetic expressions of multiplication take the following form: a digit (d) is followed by the operator (+), followed by another digit d, and possibly followed by the operator and another digit etc. For example the strings d+d, d+d+d, d+d+d+d etc. are all valid expressions. Design a DFA which accepts strings which form valid expressions. [5 marks]