Monotone and Nonmonotone Dataaow Networks

The expressiveness of concurrent data ow primitives have been studied from the point of view of automata theory [19] as well as in terms of abstractly given processes de ned in terms of traces [20]. The expressiveness of the merge primitives, fair merge, angelic merge and in nity-fair merge were shown to hinge on monotonicity properties of their trace languages. From the point of view of concurrent automata an important class of automata called monotone automata were de ned and it was shown that fair merge could not be implemented by such an automaton. In this paper we study the relationship between monotonicity properties of automata and of trace languages. We characterize the trace languages computed by monotone automata and we show that the characterization does not correspond to the existing monotonicity properties of trace languages. These, relatively easy, results led us to discover a new indeterminate primitive, the fair stack, that turns out to be nonmonotone and to have interesting expressiveness properties. We show that a fair stack is strictly weaker than fair merge but provably incomparable with angelic merge. These results suggest that it is time to study seriously the class of nonmonotone automata.

[1]  Prakash Panangaden.  McCarthy's Amb Cannot Implement Fair Merge , 1988, FSTTCS.

[2]  Joost N. Kok.  Denotational Semantics of Nets with Nondeterminism , 1986, ESOP.

[3]  Gilles Kahn,et al.  The Semantics of a Simple Language for Parallel Programming , 1974, IFIP Congress.

[4]  Prakash Panangaden,et al.  Computations, Residuals, and the POwer of Indeterminancy , 1988, ICALP.

[5]  M. W. Shields,et al.  Behavioural Presentations , 1988, REX Workshop.

[6]  Prakash Panangaden,et al.  The Expressive Power of Indeterminate Dataflow Primitives , 1992, Inf. Comput..

[7]  Prakash Panangaden,et al.  Stability and Sequentiality in Dataflow Networks , 1990, ICALP.

[8]  Eugene W. Stark.  Connections between a Concrete and an Abstract Model of Concurrent Systems , 1989, Mathematical Foundations of Programming Semantics.

[9]  Bengt Jonsson,et al.  A fully abstract trace model for dataflow networks , 1989, POPL '89.

[10]  Marta Kwiatkowska,et al.  Fairness for non-interleaving concurrency , 1989 .

[11]  Prakash Panangaden,et al.  Abstract Interpretation and Indeterminacy , 1984, Seminar on Concurrency.

[12]  Jeremy Gunawardena,et al.  Causal automata , 1992, Theor. Comput. Sci..

[13]  N. Klarlund.  Progress Measures and Finite Arguments for Infinite Computations , 1990 .

[14]  Henk Barendregt,et al.  The Lambda Calculus: Its Syntax and Semantics , 1985 .

[15]  Prakash Panangaden,et al.  Semantics of Networks Containing Indeterminate Operators , 1984, Seminar on Concurrency.

[16]  Eugene W. Stark,et al.  Concurrent Transition Systems , 1989, Theor. Comput. Sci..

[17]  Nancy A. Lynch,et al.  A Proof of the Kahn Principle for Input/Output Automata , 1989, Inf. Comput..

[18]  Alexander Moshe Rabinovich,et al.  Nets of processes and data flow , 1988, REX Workshop.

[19]  Samson Abramsky,et al.  A Generalized Kahn Principle for Abstract Asynchronous Networks , 1989, Mathematical Foundations of Programming Semantics.

[20]  Gilles Kahn,et al.  Coroutines and Networks of Parallel Processes , 1977, IFIP Congress.

[21]  James R. Russell,et al.  Full abstraction for nondeterministic dataflow networks , 1989, 30th Annual Symposium on Foundations of Computer Science.