## A fixpoint theory for non-monotonic parallelism (2002)

Citations: | 7 - 5 self |

### BibTeX

@MISC{Chen02afixpoint,

author = {Yifeng Chen},

title = {A fixpoint theory for non-monotonic parallelism},

year = {2002}

}

### OpenURL

### Abstract

This paper studies parallel recursion. The trace specification language used in this paper incorporates sequential,j nondeterminism, reactiveness(inclvenessg,F'k traces), three forms of paral'VgJj (inclVgJjqMkEglglgl fair-interlkEglgl synchronous paralonousg and general recursion. In order to use Tarski's theorem to determine the fixpoints of recursions, we need to identify awelVjgJ,FIq partial order.Several orders are considered,incldered new order calrg the lexical order, which tends tosimulM, the execution of a recursion in asimilk manner as the EglVqgJ,E, order. A theorem of this paper shows that no appropriate order exists for the lhegIIIE Tarski's theoremalor is not enough to determine the fixpoints ofparalVI recursions. Instead of usingTarski's theoremdirectl, we reason about the fixpoints of terminatingand nonterminatingbehavioursseparateli Such reasoningis supported by the leg of a new compositioncalio partition. We propose a fixpoint techniquecalni the partitioned fixpoint, which is thelgqk fixpoint of the nonterminatingbehaviours after the terminatingbehaviours reach their greatest fixpoint. The surprisingresul is thataltg,M, a recursion may not beljV"EgJqVE' monotonic, it must have the partitioned fixpoint, which isequal to thelegj lgjIjI,gJqF' fixpoint. Since the partitioned #xpoint iswel defined in anycompl,q lmpl,q theresulq areappljFMgJ to various semanticmodeli Existing fixpoint techniques simpl becomespecial cases of the partitioned fixpoint. Forexamplj an EglIIqgJq',EFglEFg recursion has itslsgj EglMMFIgJq fixpoint, which can be shown to be the same as the partitioned fixpoint. The new technique is moregeneral than thelegq EglEEkIgJq fixpoint in that the partitioned fixpoint can be determined even when a recursion is notEglVjjVgJq monotonic.Exampln of non-monotonic recur...

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