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Speculative optimizers of modern compilers are designed on techniques for probabilistic static analyses of programs. For imperative and object-oriented multi-core programs, this paper focuses on the problem of revealing probabilistic dangling references. This important problem is treated in this paper via type systems. Besides being simply structured, the type systems provide suitable frameworks for proof-carrying code applications. One class of such applications is that ofmobile codes having limited resources.Using the proposed technique, each analysis case is supported by a correctness proof in the form of a type derivation. Most important concurrent constructs such as fork-join constructs, conditionally spawned cores, and parallel loops are treated in this paper. This is done for both of imperative and objectoriented parallel programs. The paper proves the soundness of presented techniques using a probabilistic operational semantics for the language models.

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