Creating Buchi Automaton to Accept Property

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Homework Statement

Give a buchi automaton that accepts the following property
either p is true forever, or p is true until q becomes true

Homework Equations

check my answer if its right and correct if wrong

The Attempt at a Solution

Three states. Goes to p it loops and its final state.
or goes p then loops and if then goes q its final state and accepted

 

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Three states.
S0, S1 AND S2.
S1 AND S2 ACCEPT STATES
FROM S0 TO S1 IF IT IS P AND NOT Q . FROM S1 TO S2 IF IT IS( P NOT Q) OR (NOT P AND Q)

FROM S0 TO S2 IF IT IS P AND Q .
ON S1 IT LOOPS IF IT IS P AND NOT Q.
S2 LOOPS FOR EVERYTHING

 

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S0 Is The Start State

Hope I Solved Everything Right.please Correct Me