Robert M. Keller. Denotational models for parallel programs with indeterminate operators. In Neuhold, editor, Formal Descriptions of Programming Concepts, pages 337--366. North-Holland, 1978.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....(or automata) automatically. Our framework does not currently provide such a convenient method for specifying abstractions; this is a direction for future work. 5. 2 Inter channel orderings Because MFGs do not describe inter channel orderings, our analysis su#ers (in e#ect) from the merge anomaly [Kel78, Bro88]. Specifically, an input output function representing a non strict process cannot (in general) represent the process s behavior exactly; generally, the input output function must be a conservative approximation. One way to remedy this would be to augment MFGs with a partial ordering that can ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal Description of Programming Concepts, pages 337--366. North Holland, 1978.

....right hand sides. The semantic mapping F gives a set of stream processing functions F[ agent f j : ES end] N N ; which is taken to be the meaning of f . This approach is consistent with functional component specifications. It avoids the well known anomalies (see [Kel78] BA81] that appear when a relational semantics is used. Such a semantics assigns relations or set valued functions to nondeterministic declarations. 4.2. An Applicative Language 53 Based on the semantic mapping F it is easy to define when an AL component declaration refines a functional ....

R.M. Keller. Denotational models for parallel programs with indeterminate operators. In E.J. Neuhold, editor, Formal Description of Programming Concepts, pages 337--366. North Holland, 1978.

....of the output channels build the set O. 13 The reason for working with infinite histories is that if no action is communicated along an input channel within a time unit, then an empty message sequence occurs in the input history. The lack of this timing information causes the fair merge anomaly [Kel78] The functions should behave similar to deterministic automata, i.e. they should process their input incrementally. Definition 8 (Pulse driven functions) Stream processing functions whose output until time j (j 1) is completely determined by the input until time j are called weakly ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....nontrivial task. In the history based approach, the replacement of functions with input output relations leads to a non compositional model, as shown in [BA81] The replacement of functions with sets of functions, leads to a compositional model which is however too restrictive, because as shown in [Kel78], it cannot express nondeterministic fair merge components. In the statebased approach, there is no obvious way how to compose automata. One attempt is to take all possible synchronized interleavings, as done for I O automata [LT89] However, this departs from the original intuition and fails to ....

....reason for working with infinite histories is that if no action is communicated along an input channel within a time unit, then an empty message sequence occurs in the input history informing the function that time has progressed. The lack of this timing information causes the fair merge anomaly [Kel78]. The functions should behave similar to deterministic automata i.e. they should process their input incrementally. Definition 12 (Pulse driven functions) Stream processing functions whose output until time j (j 1) is completely determined by the input until time j are called weakly (strongly) ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978. 24

....channel, otherwise the special value is transmitted. Such a process provides the capability of branching on the availability of input data. In [21] a denotational semantics is sketched for networks that execute programs using polling. It is easy to see that with poll one can implement fair merge [17] and vice versa. The relation poll is not lower monotone nor is it limit closed. Finally the fmerge relation is neither lower monotone nor limit closed. 3 Residuals In this section we develop the technical machinery needed for the expressiveness proofs. Definition 11 A residual operation on an ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. Neufeld, editor, Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....behavior) can be represented. However, nondeterminate processes such as merge, which merges streams of data values arriving on two input channels into a single output stream, are also interesting and important in applications. Attempts to extend Kahn s model to the nondeterminate case, e.g. [Kel78,BA81,Par82,Pra82,Fau82,BM82,Bro83,KP84], SN85,Kok86] have not been entirely successful. To satisfactorily resolve the problem of semantics of nondeterminate process networks, not one, but two mathematical models, an operational and a denotational model, are necessary, along with a mapping that takes each object of the operational ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal Description of Programming Concepts, pages 337--366, North-Holland, 1978.

....b P P G2 P P P b loop P:b P G1 G= b P G = G1 [ G2 P;G P;G b P1 P = P1 P2 P2 Figure 5: Syntax diagram correspondence. 4.2. 2 Action Semantics Action computation obeys a well known dataflow paradigm, the semantics and properties of which have been studied extensively, e.g. [4, 5]. For our purpose, it is sufficient to denote an action a as a continuous function of a particular kind: Given a set V of variables and a set Val of basic values, the denotation of a is a function [ a] St (fl(a) Val) where St = V Val is the set of states, fl(a) is the set of ....

Robert Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal description of Programming Concepts, pages 337--363. North Holland, 1978.

....a constructive manner. This is not technically difficult, but nevertheless quite tedious. The use of streams to model dataflow networks was first proposed in [Kah74] Timed streams and relations on timed streams are also well known from the literature [Par83] Kok87] The same holds for oracles [Kel78] AL88] called prophecy variables in the latter) The presented approach is based on [BS96] which can be seen as a complete rework relational reformulation of [BDD 93] There are also some obvious links to Z [Spi88] 515 9 Acknowledgements The author has benefited from discussions with ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

.... Since Kahn s influential paper on the modeling of deterministic data flow networks was published in 1974 [Kah74] a number of authors have proposed formalisms for the representation of reactive systems based on asynchronous communication via unbounded, directed channels (see for example [Kel78] BA81] Par83] Kok87] Jon87] LT87] BDD 93] The unboundedness assumption is very useful when specifying and reasoning about systems at an abstract level. However, at some point in a development this assumption must be discharged in the sense that the communication is synchronized ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....named communication histories for its output channels. Note that if no message is communicated along an input channel within a time unit then the empty stream, represented by ffl, occurs in the communication history for that channel. The lack of this information causes the fair merge anomaly [Kel78] The functions process their input incrementally at any point in the time, their output is not allowed to depend on future input. Functions satisfying this constraint are called weakly guarded. If the output they produce in time unit t, is not only independent of future input, i.e. the ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....something out. As already highlighted by the Greek philosopher Zenon more than 2400 years ago, when something is left out we may get some strange effects often referred to as anomalies. Two very famous anomalies known from stream based models for concurrent systems is the merge anomaly [Kel78] and the Brock Ackermann anomaly [BA81] They can be summarized as follows: ffl A fair merge component merging two untimed streams into a new untimed stream containing all the messages of the argument streams cannot be represented by a prefix monotonic function. ffl Relations on untimed streams ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. NorthHolland, 1978.

....and of the input, which we have abstracted. Again, the abstraction shows up as nondeterminism. It may be an interesting excercise for the reader to convince himself that the above specification yields the intended meaning for the M operator and does not lead to the classical merge anomalies [1,13]. The example is discussed in more detail in [23] Finally, we can mention that the close relation between nondeterministic terms and sets makes it possible to use the former to define and handle subsorting directly at the term level. This is the basic intuition behind the framework of unified ....

Keller, R.M., "Denotational models for parallel programs with indeterminate operators", in Formal Descriptions of Programming Concepts, North-Holland, Amsterdam, 1978.

....is of course also planned. However, since the sequential implementation of functional languages is quite well understood, we have so far concentrated on the implementation of the network definitions. 4 The Development Method Focus Focus is a general framework, in the tradition of [Kah74] Kel78] for the formal specification and development of distributed systems. A system is modeled by a network of agents communicating asynchronously via unbounded FIFO channels. A large number of different reasoning styles and techniques is supported (see for example [BDD 92] Bro92c] Bro92a] ....

....arise when higher order messages are allowed, for example whether the whole program should be transferred or just a pointer to the (shared) code and some status information. It is well known that certain weakly time dependent agents like fair merge are hard to express in a functional setting [Kel78] One straightforward way to handle this problem in HOPSA is to incorporate a specific fair merge construct [Bro88] This construct characterizes an agent performing a fair merge of the messages received on its input channels. This construct can be modeled in the same way as any other HOPSA agent ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

.... relates two automata with distinct output sets. The full abstraction problem for machines is the problem of characterizing the structure of the quotient algebra of machines modulo observable equivalence. The difficulty of this problem has become apparent since it was first pointed out by Keller [18] and more conclusively by Brock and Ackerman [7] the so called Brock Ackerman anomaly ) that the mapping taking machines to their input output relations is not homomorphic with respect to feedback. Since then, a number of researchers [31, 32, 3, 19, 34, 20] have proposed process models that ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal Description of Programming Concepts, pages 337--366, North-Holland. 1978.

....the proposed formalism to specify a so called Min Max Component. In a step wise fashion we refine this specification into a functional program. Finally we outline how this program can be translated into SDL. 1 Introduction Focus [BDD 92a] is a general framework, in the tradition of [Kah74] Kel78] for the formal specification and development of distributed systems. A system is modeled by a network of components working concurrently, and communicating asynchronously via unbounded FIFO channels. A number of reasoning styles and techniques are supported. Focus provides mathematical ....

....which means that they do not have occurrences of p s. From a user s point of view our specifications are completely untimed. The reason why we use sets of timed stream processing functions instead untimed stream processing functions in the denotation is the well known fair merge problem [Kel78] a certain class of weakly time dependent components, like fair merge, cannot be modeled by a set of untimed stream processing functions. With the denotation used here, where we only constrain the behavior for complete (infinite) input, this is no longer a problem. The ticks allow us to ....

[Article contains additional citation context not shown here]

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....processes need not have functional behaviors. There have been many attempts to generalize Kahn s theory to a class of indeterminate networks. The obvious idea of generalizing functions to relations fails to give results consistent with token pushing semantics. This fact was first noticed by Keller [16], and subsequently became known as the Brock Ackerman anomaly, after Brock and Ackerman [7] demonstrated convincingly by some clever examples that no denotational semantics based on set theoretic input output relations can give results consistent with token pushing semantics. Subsequently, a ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal Description of Programming Concepts, pages 337--366, North-Holland. 1978.

....its output channels. Note that if no message is communicated along an input channel within a time unit then the empty stream occurs in the communication history for that channel informing the function that time has progressed. The lack of this information causes the famous fair merge anomaly [Kel78] A stream processing function is said to be weakly pulse driven if its input until time j completely determines its output until time j. It is said to be strongly pulse driven if its input until time j completely determines its output until time j 1. Formally: Definition 3 (Pulse driven ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. NorthHolland, 1978.

....anomaly. We give refinement rules which allow specifications to be decomposed into networks of specifications. 1 Introduction Dataflow components can be specified by formulas with a free variable ranging over domains of continuous functions so called stream processing functions [Kel78] BDD 92] Both time independent and time dependent components can be described this way. In the latter case, the functions are timed in the sense that the input output streams may have occurrences of a special message representing a time signal. For such specifications elegant refinement ....

....is an agent which outputs a fair merge of the messages it receives on two input channels. It is well known that, because of the continuity constraint imposed on stream processing functions, a fair merge component cannot be modeled by a set of (monotonic) untimed stream processing functions [Kel78] On the other hand, to specify components of this type in terms of timed stream processing functions is a bit like shooting sparrows with a shotgun, since explicit timing is not needed in order to characterize their behavior. In an attempt to abstract from unnecessary time dependency, this paper ....

[Article contains additional citation context not shown here]

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....case of nondeterministic dataflow networks. In such networks, the components are capable of making arbitrary choices during computation and the input output behaviour specified by such a network is not longer a function, but an arbitrary relation. For such networks, fundamental results by Keller [Kel78] and Brock Ackermann [BrA81] have shown a mismatch between the operational meaning of the networks and their input output behaviour. In other words, the input output behaviour of its components is no longer sufficient to compute the behaviour of a network. This situation, known as merge or ....

R. Keller. Denotational models for parallel programs with indeterminate operators. In: Formal description of Programming Concepts, 337--366. North-- Holland, 1986.

....We employ the proposed formalism to specify and develop a so called Min Max Component. First an overview of the whole design process is given. Then certain steps of the development are described in detail. 1 Introduction Focus [BDD 93] is a general framework, in the tradition of [Kah74] Kel78] for the formal specification and development of distributed systems. A system is modeled by a network of components working concurrently, and communicating asynchronously via unbounded FIFO channels. A number of reasoning styles and techniques are supported. Focus provides mathematical ....

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

....stream within the result. Clearly this requires the ability to check an input for the presence of data and continue on to do other things if none is present 7 rather than blocking as in Kahn s formulation. Fair merge mimics race conditions in concurrent systems and has been intensively studied [3, 4, 5, 6, 8, 9, 14, 16, 15, 22, 25, 27, 28, 29, 30]. Keller [15] was the first to remark that fair merge is not monotonic in the cpo of streams ordered by prefix (Fig. 2) 6 More precisely, the domain is the set of stream tuples ordered coordinatewise by prefix, i.e. x 1 ; xn ) is less than or equal to (y 1 ; y n ) if and only ....

....check an input for the presence of data and continue on to do other things if none is present 7 rather than blocking as in Kahn s formulation. Fair merge mimics race conditions in concurrent systems and has been intensively studied [3, 4, 5, 6, 8, 9, 14, 16, 15, 22, 25, 27, 28, 29, 30] Keller [15] was the first to remark that fair merge is not monotonic in the cpo of streams ordered by prefix (Fig. 2) 6 More precisely, the domain is the set of stream tuples ordered coordinatewise by prefix, i.e. x 1 ; xn ) is less than or equal to (y 1 ; y n ) if and only if x i is a ....

[Article contains additional citation context not shown here]

R. M. Keller. Denotational models for parallel programs with indeterminate operators. In E. J. Neuhold, editor, Formal Descriptions of Programming Concepts, pages 337--365, Amsterdam, 1978. North-Holland.

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Robert M. Keller. Denotational models for parallel programs with indeterminate operators. In Neuhold, editor, Formal Descriptions of Programming Concepts, pages 337--366. North-Holland, 1978.

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R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland,192rt 24

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R. M. Keller. Denotational models for parallel programs with indeterminate operators. In Proc. Formal Description of Programming Concepts, pages 337--366. North-Holland, 1978.

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Keller, R. M.: Denotational Models for Parallel Programs with Indeterminate Operators. Proc. Formal Description of Programming Concepts, North-Holland, (1978) 337-366

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