Discrete Mathmatics_Help
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Task Background
Automata theory involves the study of mathematical objects called automata and the computational problems that can be solved using them. Context-free grammar provides us with mathematical techniques of building phases in a language from other blocks that are smaller. Visual structures called parse trees enable us to clearly differentiate which phrases are unique and which ones are ambiguous.
Task Assignment: Below you will find a question the areas of automata. Solve the problem showing all steps. Thoroughly explain how and why you performed each step with complete sentences.
A finite-state automaton is given by the 5-tuple (Q, ∑, δ, q, F), where
Q = the finite set of states = {A, B, C}
∑ = the Alphabet (inputs) = {x, y}
δ = the transition function using the alphabet as inputs to the states
q = the initial state = {A}
F = Accepting (or final) state = {C}
The transition table for the automaton is given by:
|
|
δ |
δ |
|
|
x |
y |
|
A |
A |
B |
|
B |
A |
C |
|
C |
A |
C |
Question 1: Draw the corresponding transition diagram (digraph).
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