## The Expressive Power of Indeterminate Primitives in Asynchronous Computation (1995)

Venue: | Proceedings of the Fifteenth Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes In Computer Science |

Citations: | 6 - 2 self |

### BibTeX

@TECHREPORT{Panangaden95theexpressive,

author = {Prakash Panangaden},

title = {The Expressive Power of Indeterminate Primitives in Asynchronous Computation},

institution = {Proceedings of the Fifteenth Conference on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes In Computer Science},

year = {1995}

}

### Years of Citing Articles

### OpenURL

### Abstract

It has long been realized that the exigencies of systems programming require primitives that behave indeterminately. The best-known dataflow primitive is the so called fair merge which abstracts aspects of fair resource allocation. It has been known for about two deacdes that fair primitives lead to unbounded indeterminacy. Around seven years ago E. W. Stark, Vasant Shanbhogue and I discovered that various variants of fair merge primitives, all manifesting unbounded indeterminacy, were provably different. These differences are based on simple monotonicity properties. In the present paper I review these results and discuss some related phenomena involving a fair stack. I then describe results about fair splitting. These results are based on topological properties rather than simple order-theoretic properties. This gives some basic insight into what can and cannot be described by oracles and the relative power of various oracles. Finally I describe a result, implicitly due to Jim Russel...

### Citations

1213 |
The Lambda Calculus: its Syntax and Semantics
- Barendregt
- 1984
(Show Context)
Citation Context ...situation just outlined, the "same" b transition is enabled after the a transition but not otherwise. A rigorous treatment is based on the notion of residual [28, 42] adapted from the lambda=-= calculus [5]-=-. For our purposes we will not need the formal definitions of residuals or the algebra of residuals but the concept is important. We now introduce two important classes of automata. We say that a port... |

904 |
The semantics of a simple language for parallel programming
- Kahn
- 1974
(Show Context)
Citation Context ...put. In the present paper we review the dataflow paradigm as the arena for discussing expressiveness questions. 2 The Dataflow Paradigm The basic ideas of the dataflow paradigm go back to Gilles Kahn =-=[16]-=-. His model of distributed systems is as follows. A system is viewed as a collection of autonomous computing processes communicating by one-way, unbounded data channels. Each computing process execute... |

400 | Hierarchical correctness proofs for distributed algorithms - Lynch, Tuttle - 1987 |

278 |
Semantics of Programming Languages: Structures and Techniques
- Gunter
- 1992
(Show Context)
Citation Context ...for finite or infinite sequences, V 1 for infinite sequences and V for finite sequences of elements of V . The set V ! comes equipped with the structure of a complete partial order with least element =-=[14]-=-. The ordering is the prefix ordering and the least element is the empty sequence. The infinite elements are infinite sequence and each is the least upper bound of a chain of finite sequences. Thus V ... |

180 |
D.B.: Coroutines and networks of parallel processes
- Kahn, MacQueen
- 1977
(Show Context)
Citation Context ... in reading it, the datum is buffered indefinitely. Thus all processes are assumed receptive. An operational semantics, based on coroutines to simulate parallelism, was worked out by Kahn and McQueen =-=[17]-=-. Henceforth we refer to such networks as Kahn networks. There is an extremely pleasant mathematical description of dataflow networks. First note that a process could have an internal state. Thus one ... |

112 |
Scenarios: A model of nondeterminate computation
- Brock, Ackerman
- 1981
(Show Context)
Citation Context ...es of M as is needed with the same IO relation as N . There is a crucial point to be made here. The notion of IO Relation is not compositional. This is of course the well-known Brock-Ackerman anomaly =-=[6]. The foll-=-owing example, due to Russell [38], is more perspicuous than the original Brock-Ackerman example and relies on "weaker" primitives as we shall see later. Consider a process, shown in the lef... |

77 |
Countable Non-Determinism and Random Assignment
- Apt, Plotkin
- 1986
(Show Context)
Citation Context ...ed for bounded indeterminacy and therefore excluded the study of fair systems [32]. Several people have worked on generalizations of powerdomain techniques that would apply to unbounded indeterminacy =-=[1, 3, 7, 30, 29, 33]-=-. 3 What is Expressiveness? Three parameters are basic to any notion of expressiveness. These are 1. a notion of observation, 2. a set of primitives and 3. a collection of composition rules. Thus when... |

66 | On the semantics of fair parallelism - Park - 1979 |

59 | A Proof of the Kahn Principle for Input/Output Automata
- Lynch, Stark
- 1989
(Show Context)
Citation Context ...tions can be solved using elementary fixed-point theory. The correspondence between the operational semantics and the denotational semantics is known as Kahn's principle and has been proved many times=-=[12, 21]. A basic -=-question that arises is "what happens if we no longer have determinate primitives "? One can ask, in particular, what happens if the processes can test for the absence of data and thereby be... |

26 |
On Semantic Foundations for Applicative Multiprogramming
- Abramsky
- 1983
(Show Context)
Citation Context ...ed for bounded indeterminacy and therefore excluded the study of fair systems [32]. Several people have worked on generalizations of powerdomain techniques that would apply to unbounded indeterminacy =-=[1, 3, 7, 30, 29, 33]-=-. 3 What is Expressiveness? Three parameters are basic to any notion of expressiveness. These are 1. a notion of observation, 2. a set of primitives and 3. a collection of composition rules. Thus when... |

26 |
A fully abstract semantics for data flow nets
- Kok
- 1987
(Show Context)
Citation Context ...t the semantics is compositional and one must show that if two processes have different denotational semantics there must be a context that distinguishes them. The distinguishing contexts used by Kok =-=[19]-=- and Jonsson [15] use fair merge. This was of course before the expressiveness results were proved. 14 The question immediately arises whether something other than traces turns out to be fully abstrac... |

23 |
An operational semantics for pure dataflow
- FAUSTINI
- 1982
(Show Context)
Citation Context ...tions can be solved using elementary fixed-point theory. The correspondence between the operational semantics and the denotational semantics is known as Kahn's principle and has been proved many times=-=[12, 21]. A basic -=-question that arises is "what happens if we no longer have determinate primitives "? One can ask, in particular, what happens if the processes can test for the absence of data and thereby be... |

20 | Computations, residuals and the power of indeterminacy
- Panangaden, Stark
- 1988
(Show Context)
Citation Context ...hese automata and their fascinating theory. We refer the reader to the articles of E. W. Stark for a thorough treatment [42, 43, 44] and to his papers with the author for the expressive5 ness results =-=[28, 27]-=-. The general theory of asynchronous systems is discussed in Arnold and Nivat [4], Mazurkiewicz [23], Pratt [34], Kok [18], Kwiatkowska [20], Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The bas... |

17 | The expressive power of indeterminate dataflow primitives
- Panangaden, Shanbhogue
- 1992
(Show Context)
Citation Context ...d Nivat [4], Mazurkiewicz [23], Pratt [34], Kok [18], Kwiatkowska [20], Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata =-=[21, 26, 27]-=- are a special class of input/output automata [21]. They communicate with the environment through a fixed set of input and output ports. The automata have states and transitions between states. The ob... |

11 |
McCarthyâ€™s amb cannot implement fair merge
- Panangaden, Shanbhogue
- 1988
(Show Context)
Citation Context ...ssions and pick one of them as its result. It will only diverge if both its subcomputations diverge. It is possible to implement amerge by using amb recursively but one cannot get fair merge this way =-=[25]-=-; even though amb does embody some sort of polling. 5.2 Full Abstraction Revisited A proof of full abstraction has two parts. One has to show that the semantics is compositional and one must show that... |

10 |
Fixed point theory for communication and concurrency
- Broy
- 1983
(Show Context)
Citation Context ...ed for bounded indeterminacy and therefore excluded the study of fair systems [32]. Several people have worked on generalizations of powerdomain techniques that would apply to unbounded indeterminacy =-=[1, 3, 7, 30, 29, 33]-=-. 3 What is Expressiveness? Three parameters are basic to any notion of expressiveness. These are 1. a notion of observation, 2. a set of primitives and 3. a collection of composition rules. Thus when... |

10 | Stability and sequentiality in data flow networks - Panangaden, Shanbhogue - 1990 |

8 |
Formal computations of non deterministic recursive program schemes
- Arnold, Nivat
- 1980
(Show Context)
Citation Context ...W. Stark for a thorough treatment [42, 43, 44] and to his papers with the author for the expressive5 ness results [28, 27]. The general theory of asynchronous systems is discussed in Arnold and Nivat =-=[4]-=-, Mazurkiewicz [23], Pratt [34], Kok [18], Kwiatkowska [20], Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata [21, 26, 27... |

8 | Degrees of parallelism in the continuous type hierarchy
- Bucciarelli
- 1997
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Citation Context ...t the output on the signal channel without having it available at first. This is very closely linked to stability phenomena. In the purely determinate realm Sazanov [40] and more recently Bucciarelli =-=[8] have show-=-n that the hierarchy associated with sequential and stable functions (called "degrees of parallelism") forms a very rich structure. The monotonicity arguments that we used can be used in oth... |

8 |
Denotational semantics of nets with nondeterminism
- Kok
- 1986
(Show Context)
Citation Context ...3, 44] and to his papers with the author for the expressive5 ness results [28, 27]. The general theory of asynchronous systems is discussed in Arnold and Nivat [4], Mazurkiewicz [23], Pratt [34], Kok =-=[18]-=-, Kwiatkowska [20], Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata [21, 26, 27] are a special class of input/output aut... |

5 |
Fully abstract trace semantics for dataflow networks
- Jonsson
- 1989
(Show Context)
Citation Context ...e author for the expressive5 ness results [28, 27]. The general theory of asynchronous systems is discussed in Arnold and Nivat [4], Mazurkiewicz [23], Pratt [34], Kok [18], Kwiatkowska [20], Jonsson =-=[15]-=- and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata [21, 26, 27] are a special class of input/output automata [21]. They communicate wit... |

4 |
Metric approximations in ordered domains
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- 1985
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Citation Context ...of topology and domain theory. We collect some basic facts about the metric properties of Scott domains and how these relate to the order structure. The results are primarily due to Comyn and Dauchet =-=[9]-=-. Recall that a Scott domain is a complete partial order which is required to be (i) algebraic, (ii) have a countable basis of finite (compact) elements and finally (iii) bounded-complete (consistent ... |

4 |
Categories of Asynchronous Systems
- Kwiatkowska
- 1989
(Show Context)
Citation Context ...papers with the author for the expressive5 ness results [28, 27]. The general theory of asynchronous systems is discussed in Arnold and Nivat [4], Mazurkiewicz [23], Pratt [34], Kok [18], Kwiatkowska =-=[20]-=-, Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata [21, 26, 27] are a special class of input/output automata [21]. They c... |

3 |
A generalized Kahn's principle
- Abramsky
- 1990
(Show Context)
Citation Context ...ss is oracleizable then the IO relation is the union of a collection of functional relations. This is one approach to generalizing Kahn's principle; think of a process as realizing a set of functions =-=[2, 39]-=-. 20 Consider a process with 2 input and 4 output channels. We construct the following table. We assume that the only possible input is a 1. Input Outputs (?; ?) (1; ?; ?; ?); (?; ?; ?; 1) (1; ?) (1; ... |

2 |
The expressive power of delay operators in SCCS
- Critchlow, Panangaden
- 1991
(Show Context)
Citation Context ...and stable functions (called "degrees of parallelism") forms a very rich structure. The monotonicity arguments that we used can be used in other contexts as well. For example Critchlow and P=-=anangaden [10]-=- have used it to show that delay operators in SCCS are provably different. Similarly one can argue that one cannot implement fair merge in logic programming without some analogue of polling. Typically... |

2 |
Advanced Course in Petri Nets, volume 255
- Mazurkiewicz
- 1986
(Show Context)
Citation Context ...rough treatment [42, 43, 44] and to his papers with the author for the expressive5 ness results [28, 27]. The general theory of asynchronous systems is discussed in Arnold and Nivat [4], Mazurkiewicz =-=[23]-=-, Pratt [34], Kok [18], Kwiatkowska [20], Jonsson [15] and Rabinovich and Trakhtenbrot [35]. The basic automata that we work with are called port automata. Port automata [21, 26, 27] are a special cla... |

1 |
Nonexpressibility of signaling and fairness
- Mcallester, Panangaden, et al.
- 1993
(Show Context)
Citation Context ...this way. It is however worth understanding what different sorts of oracles are possible. In this section we give new proofs of some of the results of a paper by McAllester, Panangaden and Shanbhogue =-=[24]-=-. The results of that paper expose some of the structure of the hierarchy of expressiveness but the proofs are very operational in nature. The present 2 I am responsible. 16 proofs are due to an anony... |