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Given the LTL formula: r  pU(qOr), Write down the closure of the formula

Assignment #3 - Solution. Given the LTL formula: r  pU(qOr), Write down the closure of the formula Write down the corresponding Atoms

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Given the LTL formula: r  pU(qOr), Write down the closure of the formula

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  1. Assignment #3 - Solution Given the LTL formula: r  pU(qOr), • Write down the closure of the formula • Write down the corresponding Atoms • Develop the corresponding graph (it is recommended to employ the Tableau method), indicate the partition into acyclic s.c. sub-graphs, and a specific sub-graph that is self-fulfilling (namely makes the formula satisfiable). Closure: Cl{r  pU(qOr)} = {rpU(qOr), r(pU(qOr)), r, r, pU(qOr), (pU(qOr)), p, p, qOr, qOr, q, q, Or, Or}

  2. Extended , , and ‘next’ tables

  3. The partition into Atoms and Next relation A:{rpU(qOr), r} B:{rpU(qOr), pU(qOr), p, qOr, q} C:{rpU(qOr), pU(qOr), p, qOr, Or} D:{rpU(qOr), pU(qOr), qOr, q, Or} Next(A)=A1:{True} Next(B)=B1:{pU(qOr), p, qOr, q} B2:{pU(qOr), p, qOr, Or} B3:{pU(qOr), qOr, q, Or} Next(B1)= {B1,B2,B3} Next(B2)=B21:{pU(qOr), r, p, qOr, q} B22:{pU(qOr), r, p, qOr, Or} B23:{pU(qOr), r, qOr, q, Or} Next(B21)= {B1,B2,B3} Next(B22)= {B21,B22,B23} Next(B23)={D1} Next(B3)={D1} Next(C)= {B21,B22,B23} Next(D)=D1:{r}, Next(D1)={A1}

  4. The Tableau graph of rpU(qOr)

  5. The partition into acyclic s.c. sub-graphs, and self-fulfilling of rpU(qOr) A, A1, D1 are self-fulfilling, {B1,B2,B21,B22} is not self-fulfilling

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