Deadlocks and Dihomotopy in Mutual Exclusion Models
نویسنده
چکیده
Already in 1968, E.W. Dijkstra [Dij68] proposed to apply a geometric point of view in the consideration of coordination situations in concurrency. His progress graphs were the basis of the Higher Dimensional Automata (HDA) introduced by V. Pratt[Pra91] and developed in the thesis of É. Goubault[Gou95] and in later research (cf. [FGR99]). In this abstract, we stick to a simple continuous geometric model. A system of n concurrent processes will be represented as a subset of Euclidean space IR with the usual partial order. Each coordinate axis corresponds to one of the processes performing a linear programme; a state of the system is a point in IR with its ith coordinate describing “local time” of the ith processor. A run of a concurrent program is modelled by a continuous increasing path – time increases for every participating processor – between two states. Shared resources can often only be used by one or a limited number of processors at the same time. As a consequence, certain hyperrectangles – corresponding to conflict in the access to such a resource – have to be removed from the model; together, they form the forbidden region. The resultingmutual exclusion models are more general than those modelling semaphore programs. They allow us to consider also k-semaphores, where a shared object may be accessed by k, but not by k + 1 processors. To get more formal, let I = [0, 1] denote the unit interval, and let I ⊂ IR denote the unit hypercube. An (open) isothetic hyperrectangle is a subset
منابع مشابه
Deadlocks and Dihomotopy in Mutual Exclusion Models Deadlocks and Dihomotopy in Mutual Exclusion Models
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ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 365 شماره
صفحات -
تاریخ انتشار 2005