S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We use greek letters #, #, to denote visible actions and arabic letters a, b, to range over arbitrary actions. Definition 2. 1 A fully probabilistic system is a tuple (S, Act , P) consisting of a set S of states, a nonempty set Act of actions and a function P : S Act S # [0, 1] (called the transition probability function) such that, for each s # S, P(s, a, t) 0 for at most countably many pairs (a, t) # Act S and P a,t P(s, a, t) # 0, 1 . Let (S, Act , P) be a fully probabilistic system. S is said to be finite i# S and Act are finite. A state s of S ....

....use Q(s, L 1 . L k , # 1 . # r , t)to denote the probability of performing the string # # # 1 . # # # r ending up in state t when o#ered a string of L 1 . L k . The formal definition of Q( is as follows. Definition 3. 10 The function Q : S O#r # (Act # ) # 2 S # [0, 1] is defined as follows. Let s # S, C # S, L # O#r , # # Act # , L # O#r # , # # (Act # ) # . Q(s, # O# , #, C) 0 if # #= # Q(s, L, #, C) 8 : 1 : if s # C 0 : otherwise Q(s, L L, ##, C) X u#S Q(s, L, #, C) Q(u, L, #, C) Q(s, L, #, C) 0 if ....

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S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum (ed.), Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.

....by a unique path from the initial state) For simplicity, we restrict ourselves to finitely branching probabilistic transition systems. We define the semantic domains by recursive equations soluble in suitable categories of complete metric spaces and domains by the methods of [RT93] resp. [AJ94]. The central idea is to represent a probabilistic tree by a set of pairs (ff; where ff is an action and a distribution on probabilistic trees. More formally, our aim is to solve domain equations of the form X = Act Theta D 1 (X) where ( Delta) denotes a suitable powerdomain ....

....trees. More formally, our aim is to solve domain equations of the form X = Act Theta D 1 (X) where ( Delta) denotes a suitable powerdomain construction. Unfortunately, in both cases the equation cannot be solved by the methods of America Rutten [AR89] resp. Abramsky Jung [AJ94], since the operator D 1 ( Delta) does not preserve completeness (cf. Remark 4.6 and 4.9) Nevertheless, the equation X = fin (Act Theta D 1 (X) has a final solution in SET, the category of sets and functions (see Section 3.1) Here, fin ( Delta) denotes the collection of finite subsets of ....

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S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.

....fully abstract models for bisimulation and simulation are given on domains that are defined by recursive domain equations (e.g. 9,17,8,1,4] we define the semantic domains by recursive equations soluble in suitable categories of complete metric spaces and domains by the methods of [38] resp. [2]. The central idea is to represent a probabilistic process by a set of pairs (ff; where ff is an action and a distribution on probabilistic processes. More formally, our aim is to solve domain equations of the form X = Act Theta D 1 (X) where ( Delta) denotes a suitable powerdomain ....

....is an action and a distribution on probabilistic processes. More formally, our aim is to solve domain equations of the form X = Act Theta D 1 (X) where ( Delta) denotes a suitable powerdomain construction. Unfortunately, the standard methods of [31,32,3,33,38] in the metric case and [29,41,2] for partial order fail for the above equation since 4 Note that the only weight function for ( 1 ; 2 ) where 1 = 1 t 1 , 2 = 1 t 2 are simple distributions, is ffi(u 1 ; u 2 ) 0 if (u 1 ; u 2 ) 6= t 1 ; t 2 ) and ffi(t 1 ; t 2 ) 1. Hence, if P i = S i ; i ; s i ) are ....

[Article contains additional citation context not shown here]

S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.

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S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.

No context found.

S. Abramsky, A. Jung: Domain Theory, In S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Vol. 3, Clarendon Press, pp 1-168, 1994.

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