N. Francez: Fairness, Springer-Verlag, New York, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a restricted cumulator (Counter Counter) # R where x R y = x # I y) The first counter and the second counter count the numbers of executed wait and signal operations respectively, while I denotes the initial value of the semaphore. There are many kinds of fairness in the literature [7]. All of them require fair distribution of resources among competing consumers such that no resource can be kept cumulating at the expense of another resource s exhaustion. Definition 5 (Fair product) The fair product of C and C # is defined by C# = x =#) y # =#) Example. The ....

Francez, N., "Fairness," Springer-Verlag, 1986.

....in the sense of Ochsenschl ager. Keywords. Veri cation, Relative Liveness Properties, Behavior Abstraction, Simple Homomorphisms. 1 Introduction To be able to verify liveness properties of a system [3] it is almost always necessary to include a fairness hypothesis in the system description [9]. Indeed, introducing a fairness hypothesis makes it possible to ignore behaviors that correspond to extreme execution scenarios and that, in any case, would not occur in any reasonable implementation. Even though this intuition is clear, making fairness precise is somewhat more complicated: ....

Francez, N. Fairness, rst ed. Springer Verlag, New York, 1986.

....through the bu#er, one constraint must be placed upon the selection of transactions for execution: every transaction present in the transaction space at any point in the computation must eventually be executed. That is, Swarm transactions must be selected for execution in a (weakly) fair manner [10]. To illustrate other characteristics of the Swarm model and notation, we can now modify the producer consumer program in various ways. Figure 2 shows a producer consumer program which 6 [I, V : 0 buf(I, V ) I, X,Y : 0 v : buf(I, v) buf(I, X) P roducer( I 1) mod N,X 1) ....

N. Francez. Fairness. Springer-Verlag, New York, 1986.

....the following tuple type declaration states this restriction: P, L, I : P ixel(P ) P ixel(L) Lo has intensity(P, I) In the Swarm syntax, a comma which separates two logical expressions has the same meaning as the (logical and) operator. This type of fairness is called weak fairness [16] or justice [21] 6 The correctness requirements remain essentially the same as for the GC program. The definitions for is labeled, adjacent, neighbors, and R require only trivial changes to accommodate the new representation. However, because in the Swarm representation more than one intensity ....

N. Francez. Fairness. Springer-Verlag, New York, 1986.

....being unfamiliar with the Buchi automaton construction procedure, do not have an intuitive understanding of the generated Buchi automaton interpreting counterexamples produced by the model checker is therefore very difficult. Another disadvantage of this method is that fairness assumptions [Fra86, MP91b] cannot be handled very well. A plausible approach to handle fairness is to express the fairness assumption as a formula F , and model check the formula F ) q , where q is the property to be checked. This approach is not very feasible because even if the original formula q expressing the desired ....

....for Eventuality 4.2.1 Example 3: Basic Response under Weak Fairness (a) Proof Rule for 2(p ) 3q) This formula asserts that every state s i where formula p holds is followed by a state s j (j i ) where formula q holds. Response properties are usually established under a fairness assumption [Fra86, MP91b]. A common fairness assumption, known as weak fairness, formalises the concept of finite progress [Dij68] if a program P has an enabled operation, then it will be eventually executed. The effect of a fairness assumption is to disallow behaviours that would otherwise be legal behaviours of ....

N. Francez. Fairness. Springer-Verlag, 1986.

.... weakness of all the available symbolic model checkers is that, in their representation of fairness, they only consider the concept of justice (weak fairness) As suggested by many researchers, another important fairness requirement is that of compassion (strong fairness) e.g. GPSS80] LPS81] Fra86] This type of fairness is particularly useful in the analysis of systems that use semaphores, synchronous communication, and other special coordination primitives. A partial answer to this criticism is that, since compassion can be expressed in ltl (but not in ctl) once we developed a ....

N. Francez. Fairness. Springer-Verlag, 1986. 101

....from the final state of x ffl If x is infinite then either actions from X appear infinitely often in x or states from which no action of X is enabled appear infinitely often in x A finite fair execution is also said to be quiescent. The notion of fairness defined above recalls weak fairness [Fra86] but the two concepts are different. In [Fra86] fairness is considered for each action, while in I O automata fairness is considered for locally controlled actions only. Moreover, instead of considering single actions, fairness is defined in terms of sets of actions within I O automata. The idea ....

....then either actions from X appear infinitely often in x or states from which no action of X is enabled appear infinitely often in x A finite fair execution is also said to be quiescent. The notion of fairness defined above recalls weak fairness [Fra86] but the two concepts are different. In [Fra86] fairness is considered for each action, while in I O automata fairness is considered for locally controlled actions only. Moreover, instead of considering single actions, fairness is defined in terms of sets of actions within I O automata. The idea behind the partition of locally controlled ....

Nissim Francez. Fairness. Springer-Verlag, Berlin, 1986.

....semantics and processes must be considered together with their admissibility sets. A suitable individuation principle for processes must also be sensitive to differences of admissibility sets. The finite delay approach to fairness has received some criticism for being ad hoc (see Francez [10]) in the sense that the calculus in itself leaves no room for fairness considerations which are only introduced at the level of the operational semantics. A drawback with the finite delay calculus, already pointed out by Milner in [21] is also the fact that a unique fixpoint theorem necessarily ....

N. Francez, Fairness, Springer-Verlag, 1986.

....introduced by Lehmann, Pnueli and Stavi [LPS81] for shared variables programs, and by Queille and Sifakis [QS83] for transition systems. Its traditional uses include the modeling of concurrency and of un biased arbitration; among the monographs devoted to the study of fairness, we recall Francez [Fra86] and Apt, Francez and Katz [AFK88] Two notions of fairness are commonly considered: justice, also called weak fairness, and compassion, also called strong fairness (see Manna and Pnueli [MP91, MP95] Informally, the meaning of justice and compassion can be described as follows. If is a just ....

N. Francez. Fairness. Springer-Verlag, 1986.

.... out in [dNV 90] An interesting question is whether a similar characterization can be shown for weak bisimulation [Milner 90] Many proof rules for temporal properties are based on well foundedness arguments, especially those for termination of programs under fairness constraints (cf. GFMdR 83, Francez 86, AO 92] Vardi [Vardi 87] and Klarlund and Kozen [KK 91] develop such proof rules for very general types of linear temporal properties. Our use of well foundedness arguments for defining a bisimulation appears to be new, and, we believe, of intrinsic mathematical interest. The motivation in ....

Francez, N. Fairness. Springer Verlag, 1986.

....infinite behaviours are completely determined by the finite behaviours. However in semantics for concurrent systems, it is often the case that some infinite computations are considered as inadmissible, even if all finite parts of them are admissible, referring to some kind of fairness condition [39]. This leads us to consider models allowing an explicit representation of infinite computations. The first approaches to semantics of fair concurrency were inspired by language theory, using # languages or (variations of) Buchi automata [104] Later more direct extensions of the traditional models ....

....[57] 3.2 Fairness Fairness is a property of completed computations: a typical fairness property asserts that something (good) will eventually happen during the computation , which of course cannot be judged without observing the complete computation. As e.g. described in the book of Francez [39] there is a large number of di#erent notions of fairness. The work presented making fairness a liveness property in the sense of [79] 23 in Ch. 7 does not in particular focus on how computations are deemed unfair, but follow the line of work in e.g. 54, 7] and consider models that more ....

N. Francez. Fairness. Springer-Verlag, 1986.

....occur. Continuous enabledness means that the respective processor and all other resources are always available, and in a parallel system such an independent processor will certainly act eventually. Thus, our sort of fairness is met automatically, it does not have to be implemented; see [Fra86] for more on fairness. After the de nition, we will determine a compositional semantics suitable for dealing with our sort of fairness. In [Vog97] we de ned a fair semantics and determined the coarsest compositional re nement of it for safe nets. This result does not directly carry over to ....

....not directly carry over to general nets, but it can be generalized when we use a slightly peculiar de nition of fairness; we will discuss this peculiarity in detail after the de nition. t t Figure 1 But rst, we have to discuss the impact of read arcs on the progress assumption. Classically [Fra86], an in nite ring sequence MN [t 0 iM 1 [t 1 iM 2 : would be called fair if we have: if some transition t is enabled under all M i for i greater than some j, then t = t i for some i j. With this de nition, the sequence t of in nitely many t s would not be fair in the net of Figure 1, ....

N. Francez. Fairness. Springer-Verlag, 1986.

....Str. Academiei 14, 70109 Bucharest, Romania Abstract. The paper deals with a new type of restriction considered for the cooperation protocol of grammar systems. The e ect of this strategy is investigated for all modes of derivation. Some connections are made with the usual concepts of fairness [1, 6] and that introduced for grammar systems [5] 1 Introduction The cooperating distributed (CD for short) grammar system was introduced rst in [9] with motivations related to two level grammars. An intensive study of CD grammar systems has been started after relating them with arti cial ....

....rules. Moreover, if there are more neglected components at a given moment, then the most neglected is selected as active component, having the highest priority. This approach has some links with the fairness concepts introduced and studied in relation with the behavior of parallel processes [1] [6]. Our concept is di erent from the strategies used in [5] due to the fact that a component which had no opportunity to apply its rules does not disturb the derivation process. Informally, we associate to each component P an integer variable v to hold the di erence between the number of ....

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N. Francez. Fairness. Springer-Verlag, 1986.

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N. Francez. Fairness. Springer-Verlag, 1986.

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N. Francez. Fairness. Springer-Verlag, New York, 1986.

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N. Francez. Fairness. Springer-Verlag, New York, 1986.

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N. Francez. Fairness. Springer-Verlag, 1986.

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