By Roland Meyer, André Platzer, Heike Wehrheim
This e-book is devoted to Professor Ernst--Rüdiger Olderog at the party of his sixtieth birthday. This quantity is a mirrored image on Professor Olderog's contributions to the clinical neighborhood. It offers a pattern of analysis rules which were prompted at once by way of Ernst-Rüdiger Olderog's paintings. After a laudatio part that gives a short evaluation of Ernst-Rüdiger Olderog's study, the publication is made from 5 components with medical papers written by way of colleagues and collaborators of Professor Olderog. The papers handle semantics, approach algebras, logics for verification, application research, and synthesis approaches.
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Additional info for Correct System Design: Symposium in Honor of Ernst-Rüdiger Olderog on the Occasion of His 60th Birthday, Oldenburg, Germany, September 8-9, 2015, Proceedings
Stated in words, this result asserts that the weakest-pre-expectation of program P in initial state σI wrt. post-expectation f coincides with the expected reward in the MDP of P where reward f is assigned to successfully terminating states. For probabilistic programs with observations but without non–determinism we can establish a correspondence between the conditional expected reward on the MDP of a program and its conditional pre–expectation: Understanding Probabilistic Programs 29 Theorem 2 (Transfer theorem for conditional expectations ).
Again, every ﬁnite execution is trivially fair. Thus we concentrate on inﬁnite executions throughout this paper. 1 In the literature, this notion of fairness is qualiﬁed as strong fairness (or compassion). For brevity, we simply refer to this notion without the qualiﬁer in this paper. 38 J. Hoenicke and A. , there exist fair executions in this case. 3 Explicit Scheduling We extend the deﬁnition of a scheduler from  to the setting of inﬁnitary control. In a given state σ the scheduler inputs a set C of created processes and a subset E ⊆ C of enabled processes.
1007/978-3-319-23506-6 6 Evaluation Trees for Proposition Algebra 45 Table 1. The set CP of equational axioms for free valuation congruence x x (y T y=x x F y=y T x F=x z u) v = (x y v) z (x u v) (CP1) (CP2) (CP3) (CP4) is “if Q then P else R”, but in order to reason systematically with conditional statements, a notation such as P Q R is preferable. In a conditional statement P Q R, ﬁrst Q is evaluated, and depending on that evaluation result, then either P or R is evaluated (and the other is not) and determines the ﬁnal evaluation result.