Cohomologie cristalline des schemas de caracteristique p O by P. Berthelot

By P. Berthelot

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The set L is ranged over by P, Q, . .. As usual in security models, we distinguish among high level visible actions and low level visible actions by defining two disjoint sets ATypeH of high level types and ATypeL of low level types that form a covering of AType − {τ }, such that a ∈ GAct and a∗ ∈ RAct are high (low) level actions if a ∈ ATypeH (a ∈ ATypeL ). Now, we give an informal intuition of the operators, while we delay a complete presentation of their semantics to the appendix. – 0 represents the terminated or deadlocked term.

The choice within a bundle is purely probabilistic, while the choice among bundles is nondeterministic. Formally, AType denotes the set of action types, ranged over by a, b, . , including also the special type τ denoting an internal action. We denote the set of reactive actions by RAct = {a∗ | a ∈ AType − {τ }} and the set of generative actions by GAct = AType (note that τ is a generative action, because it expresses an autonomous internal move that does not react to external stimuli). The set of actions is denoted by Act = RAct ∪ GAct , ranged over by π, π , .

We consider only CTMCs with one absorbing state. We assume an n-state absorbing Markov chain with generator matrix    Q=  T0    0 ··· 0 0 T (1) and starting distribution π = (π1 , . . , πn ). The last row of the matrix represents the absorbing state, and T0 all transition that go into this state. The representation of the phase-type distribution is defined to be the tuple (α, T), where α = (π1 , . . , πn−1 ). In this paper, we have to consider both the generator matrices as well as the representations of phase-type distributions.

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