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Abstract: Certain behavioral properties of distributed systems are difficult to express in interleaving semantics, whereas they are naturally expressed in terms of partial orders of events or, equivalently, Mazurkiewicz traces. Two examples of such properties are serializability of a database and global snapshots of concurrent systems. Recently, a modest extension for LTL by an operator that expresses snapshots, has been proposed. It combines the ease of linear (interleaving) specification with this useful partial order concept. The new construct allows one to assert that a global snapshot appeared in the past, perhaps not in the observed execution sequence, but possibly in an equivalent one. Originally, a model checking algorithm for this logic that is exponential space in the size of the system was suggested. In this paper, we provide a model checking algorithm that is in polynomial space in the size of the system. Our construction can also serve as an efficient (polynomial) algorithm for detecting conjunctive properties (i.e., conjunction of local process properties) in a concurrent history of execution. [Copyright &y& Elsevier]

Abstract: The advent of proof-carrying code has generated significant interest in reasoning about low-level languages. It is widely believed that low-level languages with jumps must be difficult to reason about because of being inherently non-modular. We argue that this is untrue. We take it seriously that, unlike statements of a high-level language, pieces of low-level code are multiple-entry and multiple-exit. And we define a piece of code as consisting of either a single labelled instruction or a finite union of pieces of code. Thus we obtain a compositional natural semantics and a matching Hoare logic for a basic low-level language with jumps. By their simplicity and intuitiveness, these are comparable to the standard natural semantics and Hoare logic of While. The Hoare logic is sound and complete wrt the semantics and allows for compilation of proofs of the Hoare logic of While. [Copyright &y& Elsevier]