W. W. Wadge, An extensional treatment of dataflow deadlock, Theoretical Computer Science 13 (1981). 16  Home/Search   Document Not in Database   Summary   Related Articles   Check

....quasi pseudo metric space. Weighted spaces We recall that the generalized metric spaces known as the weightable quasi pseudometric spaces have been introduced by Matthews in [Mat94] and [Mat92a] as part of 5 the study of the denotational semantics of dataflow networks (cf. also [Kah74] and [Wad81]) Definition 2 A quasi pseudo metric space (X, d) is weightable i# there exists a function w: X 0 such that X. d(x, y) w(x) d(y, x) w(y) The function w is called a weighting function, w(x) is the weight of x and the quasi pseudo metric d is weightable by the function w. A weighted ....

....segment and # = 0 otherwise. The function p is a partial metric , that is a generalized metric which does not necessarily satisfies the axiom of reflexivity #x. p(x, x) 0 . The function is also referred to as the Baire partial metric or the Kahn partial metric (e.g. Kah74] Mat92a] and [Wad81]) We recall that any partial metric p can be replaced by a weightable quasi pseudo metric d which induces the same topology, where d is defined by: d(x, y) p(x, y) p(x, x) and where a weighting function for d is given by the function w(x) p(x, x) cf. Mat94] The above examples, except ....

W. W. Wadge, An extensional treatment of dataflow deadlock, Theoretical Computer Science 13 (1981). 16

....19] In addition, it is highly desirable to develop techniques whereby forming cyclic connections can be automated to some extent, perhaps under certain conditions. The use of variants as in Roscoe and Daithi s work [23] may provide some clues. Another possibility is the cycle sum test of Wadge [26]. Future work will include applications of these ideas to more substantial examples, perhaps illustrating the use of successful termination. Although we have focused on deadlock freedom in this paper, specification structures allow other properties such as fairness and liveness to be added in the ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981. 20

....temporal logic programs that are locally stratified. A locally stratified program is guaranteed to have a unique intended model, which is called the perfect model of this program. The test has been named cycle sum test, as is has been inspired by the homonymous test proposed by W. W. Wadge [Wad81] for detecting deadlocks in the context of dataflow programming. The test of [Ron01] constructs the so called cycle sum graph, a labeled directed graph whose nodes are program predicates. In this graph, there is an edge from a predicate p to a predicate q whenever there is a program clause whose ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

....logic programs depends on an implicit time parameter which needs to be taken into consideration or otherwise most programs would have to be rejected. In other words, an effective stratification test for temporal logic programming should also examine for temporal circularities in the program. In [Wad81] W. Wadge developed the cycle sum test which ensures that a given temporal functional program of the language Lucid [WA85] is deadlock free. The test was later extended by S. Matthews [Mat95] to a wider context (but still in the area of functional programming) We show that the test is also ....

....given a time classical logic program P , there is a close relationship between the structure of the cycle sum graph CGP and the dependency graph DGP . This relationship is reflected by the following Lemma: 3 However, notice that programs such as the above in fact contain some form of deadlock [Wad81] and are in a sense against the spirit of temporal logic programming which views predicates as infinite streams [Wad88] 8 Lemma 5.1 Let P be a time classical logic program. Then, a directed walk in DGP corresponds to a directed walk in CGP . Proof: Let v 0 e 1 v 1 Delta Delta Delta e n ....

W. W. Wadge. An Extensional Treatment of Dataflow Deadlock. Theoretical Computer Science, 13:3--15, 1981.

....the streams are finite in length, then the program must terminate. Otherwise, the program never terminates and produces at least one infinite stream of data. Termination is determined completely by the definitionof the process network and is not affected by the particular choice of execution order [44]. The least fixed point solution determines the length of every stream, but it does not determine the order in which the stream elements are produced. Consequently there are many possible execution orders that can lead to the least fixed point. A complete execution of a Kahn process network ....

W. W. Wadge. An extensional treatment of dataflow deadlock. In Semantics of Concurrent Computations, pages 285--299, Evian, France, July 1979.

....19] In addition, it is highly desirable to develop techniques whereby forming cyclic connections can be automated to some extent, perhaps under certain conditions. The use of variants as in Roscoe and Daithi s work [23] may provide some clues. Another possibility is the cycle sum test of Wadge [26]. Future work will include applications of these ideas to more substantial examples, perhaps illustrating the use of successful termination. Although we have focused on deadlock freedom in this paper, specification structures allow other properties such as fairness and liveness to be added in the ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981. 20

....on a higher order semantics, we argue that languages based on this approach are inappropriate as abstract specification languages for STs. 2) General purpose languages mean that either invalid or incorrect or incomplete STs can be specified leading to non determinism and deadlock (see [4] and [72]) 3) The expressive power of general purpose languages means that if automatic tools for the verification of STs are to be used then in general completion algorithms such as KnuthBendix (see [37] must be applied to specifications (see [1] and [58] 4) The infinite size of streams means ....

W W Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

....for a particular operator and to decide the buffering method to be used between operators. Total and Partial Operators A total operator produces a complete data object. A complete data object is one which does not contain bottom, i.e. it has no holes or gaps, and it cannot be further completed [7]. A partial operator is one which may produce an incomplete data object when applied to complete operand values. Predictably and Unpredictably heedless Operators A predictably heedless operator is one in which the subset of inputs required to compute each result can be predicted syntactically; ....

W. W. Wadge, "An extensional treatment of dataflow deadlock," in G. Kahn (editor), Lecture Notes in Computer Science: Semantics of Concurrent Computation, Springer-Verlag, pp. 285299, 1979.

....formation is restricted so that every cycle contains a pre node; the pre operator in Lustre introduces an output which is independent of one input. Hence any legal cycle in a Lustre program satisfies our condition. Furthermore, our condition is the natural specialisation of Wadge s cycle sum test [47] to the synchronous case. Wadge attaches an integer weight to every path from input to output in every node, corresponding to a delay in causality. Computations of history independent functions have a weight of 0, the pre node has a weight of 1, and a node which produces output only after ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981. 64

....we have already mentioned, the lack of a generally accepted clear and straightforward semantics. 3. 5 Synchronous Dataflow The asynchronous nature of dataflow can lead to problems with non determinism and associated anomalous behaviour (see [42] and cyclic networks can suffer from deadlock (see [222] and [172] Synchronous dataflow has been developed to avoid these problems. While each filter in a synchronous dataflow network still has its own clock, rather than a global clock as the name might suggest, the interplay between these clocks is restricted and ensures synchronous (and hence ....

....via compilation into finite automata. The authors state that LUSTRE programs are subject to a strict analysis for deadlock based on a domain theoretic analysis of the various clocks defined using the When operator, rather than by the cycle sum test that is applied to Lucid programmes (see [222]) However, the authors concede that while this approach does detect any potential deadlock it also rejects some valid programmes. It is this strict approach to the interplay between the various clocks over which the various filters compute within a programme that ensures the synchronous nature of ....

W W Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

....will change the current attitude toward dataflow and the general usage of dataflow techniques. 4. 5 Synchronous Dataflow The asynchronous nature of dataflow can lead to problems with non determinism and associated anomalous behaviour (see [36] and cyclic networks can suffer from deadlock (see [164] and [124] Synchronous dataflow has been developed to avoid these problems. While each filter in a synchronous dataflow network still has its own clock, rather than a global clock as the name might suggest, the interplay between these clocks is restricted and ensures synchronous (and hence ....

....via compilation into finite automata. The authors state that LUSTRE programs are subject to a strict analysis for deadlock based on a domain theoretic analysis of the various clocks defined using the When operator, rather than by the cycle sum test that is applied to LUCID programmes (see [164]) However, the authors concede that while this approach does detect any potential deadlock it also rejects some valid programmes. It is this strict approach to the interplay between the various clocks over which the various filters compute within a programme that ensures the synchronous nature of ....

W W Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

....[26] In addition, it is highly desirable to develop techniques whereby forming cyclic connections can be automated to some extent, perhaps under certain conditions. The use of variants as in Roscoe and Daithi s work [24] may provide some clues. Another possibility is the cycle sum test of Wadge [27], which captures the idea that the presence of non trivial delays in feedback loops is a necessary condition for deadlock freedom. In any case, extra information about processes would be needed in order to automate checking of cyclic connections; we would hope to be able to define an additional ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

....no edge t) correspond to spatial recursive expression requiring a sequential implementation. An expression not appearing in a cycle is a data parallel expression. It can be computed as soon as its ancestors have been computed. Here, we are dealing with recursive definitions of collections but see [Wad81] for a similar approach which handles recursive streams and [Sij89] for recursive lists. In fact, the complete processing of the sequencing graph is a bit more complicated. We made the assumption that the calculus of the instantaneous value of X does not depend on the instantaneous value of X, ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13(1):3--15, 1981.

....difference between our handling of time and the synchronous concept of time in reactive systems. If D[ x] or C[ x] reduces to F alse, there is no value produced in the sequence V[ x] This situation is a kind of deadlock. Deadlocks detection in declarative stream definitions are studied in [35, 36] and for lazy lists in [37] Thanks to the ROBDD [38] representation of clocks, it is possible to detect at compile time some cases of such definitions. Clock reducing to T rue can also be detected and their implementation optimized. Signal has developed a sophisticated clock calculus to solve ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13(1):3--15, 1981.

....changes in the system, while clocks in reactive systems tells when the value of a signal is present. If D(x) or C(x) reduces to F alse, there is no value produced in the sequence V(x) This situation is a kind of deadlock. Deadlocks detection in declarative stream definitions are studied in [35,36] and for lazy lists in [37] Thanks to the ROBDD [38] representation of clocks, it is possible to detect at compile time some cases of such definitions. Clock reducing to T rue can also be detected and their implementation optimized. Signal has developed a sophisticated clock calculus to solve ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13(1):3--15, 1981.

....no edge t) correspond to spatial recursive expression requiring a sequential implementation. An expression not appearing in a cycle is a data parallel expression. It can be computed as soon as its ancestors have been computed. Here, we are dealing with recursive definitions of collections but see [38] for a similar approach which handles recursive streams and [39] for recursive lists. Dependency graph corresponding to the annotations The three basic annotations: Program with a spatial recursion: T S t T S p T S T.0 T.1 T.2 S.0 S.1 S.2 T.0 T.1 T.2 S.0 S.1 S.2 T.0 T.1 T.2 S.0 S.1 S.2 T.i is ....

W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13(1):3--15, 1981.

....quasi pseudo metric space. Weighted spaces We recall that the generalized metric spaces known as the weightable quasi pseudo metric spaces have been introduced by Matthews in [Mat94] and [Mat92a] as part of the study of the denotational semantics of dataflow networks (cf. also [Kah74] and [Wad81]) Definition 2 A quasi pseudo metric space (X; d) is weightable iff there exists a function w: X R 0 such that 8x; y 2 X: d(x; y) w(x) d(y; x) w(y) The function w is called a weighting function, w(x) is the weight of x and the quasi pseudo metric d is weightable by the function w. A ....

....segment and ff = 0 otherwise. The function p is a partial metric , that is a generalized metric which does not necessarily satisfies the axiom of reflexivity 8x: p(x; x) 0 . The function is also referred to as the Baire partial metric or the Kahn partial metric (e.g. Kah74] Mat92a] and [Wad81]) We recall that any partial metric p can be replaced by a weightable quasi pseudo metric d which induces the same topology, where d is defined by: d(x; y) p(x; y) Gamma p(x; x) and where a weighting function for d is given by the function w(x) p(x; x) cf. Mat94] The above examples, ....

W. W. Wadge, An extensional treatment of dataflow deadlock, Theoretical Computer Science 13 (1981).

....the definition slightly: fibs = 1 : map2 ( fibs (tl fibs) then each element after the first element depends on itself. In semantic terms, the result is simply 1 : but if the program is considered as a model of a network of concurrent processes, then the effect models deadlock (see Wadge [13]) 1 . In communication, our major concern is avoiding deadlock when the unannotated program is defined. This point becomes particularly clear when we look at a node, A, whose output is sent to two nodes, B and C . We must ensure that B does not have to wait for C to be ready to receive before B ....

W.W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13:3--15, 1981.

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W. W. Wadge. An extensional treatment of dataflow deadlock. Theoretical Computer Science, 13(1):3--15, 1981.

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