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1. We use this result (A3, 3 ) in the proof of the other implication: (A3, ~ ) . 6. 1). Let PI and P2 be P and ~ P , respectively, and let R ( X ) be X ~ ( f P = r + s ~ f P = r; f P = s). 1 and definition o f f p . To establish the inductive step R ( X ; [P]), we prove that (X; ( [ P ] A ~ = u ) ) A fP=r+s ~ (fP=r; fP=s) We consider two cases: s>_u>0: (Z; ( [ P ] / x e = u)) /x f P = r + s ( ( X A 3 x . 3,ITL (3 x. f P = x; f P = s) A f P = r + s by (*) =~ f P = r; f P = s by (A3, o) = The proof is completed by establishing the other inductive step R(X; [-~P]).

Notes in Comp. , pages 591619. Springer-Verlag, 1992. O. Maler, Z. Manna~ and A. Pnueli. From timed to hybrid systems. W. de Bakker, C. P. de Roever, and G. Rozenberg, editors, Proceedings of the REX Workshop "Real-Time: Theory in Practice", volume 600 of Lect. Notes in Comp. , pages 447-484. Springer-Verlag, 1992. Z. Manna and A. Pnueli. Completing the temporal picture. Theor. Comp. , 83(1):97-130, 1991. Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems: Specification.

Z. Manna and A. Pnueli: The Temporal Logic of Reactive and Concurrent Systems, Springer Verlag, 1992. 8. K. Marzullo: Tolerating Failures of Continuous-Valued Sensors, Technical Rep. TR90-1156, Dept. Comp. Sc. Cornell University, Itacha, NY, USA. 9. B. Moszkowski: A Temporal Logic for Multilevel Reasoning about Hardware, IEEE Computer, 18,2, pp. 10-19, 1985. 10. X. Nicollin, J. Sifakis and S. Yovine: From ATP to Timed Graphs and Hybrid Systems, in J. W. de Bakker, C. -P. de Roever and G. ) Real-Time: Theory in Practice, REX Workshop, pp.

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A Survey of Free Math Fonts for TEX and LATEX by Stephen G.Hartke


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