* Exclusion: At most one process executes its critical section at any time.

The "wait-free hierarchy" provides a classification of multiprocessor synchronization primitives based on the values of n for which there are deterministic wait-free implementations of n-process consensus using instances of these objects and read-write registers. In a randomized wait-free setting, this classification is degenerate, since n-process consensus can be solved using only O(n) read-write registers. In this paper, we propose a classification of synchronization primitives based on the space complexity of randomized solutions to n-process consensus. A historyless object, such as a read-write register, a swap register, or a test&set register, is an object whose state depends only on the last nontrivial operation that was applied to it. We show that, using historyless objects,\Omega\Gamma p n) object instances are necessary to solve n-process consensus. This lower bound holds even if the objects have unbounded size and the termination requirement is non-deterministi...

We establish a lower bound of 23 N= log log N) remote memory references for N-process mutual exclusion algorithms based on reads, writes, or comparison primitives such as test-and-set and compareand -swap. Our bound improves an earlier lower bound of 32 log N= log log log N) established by Cypher. Our lower bound is of importance for two reasons. First, it almost matches the (log N) time complexity of the best-known algorithms based on reads, writes, or comparison primitives. Second, our lower bound suggests that it is likely that, from an asymptotic standpoint, comparison primitives are no better than reads and writes when implementing local-spin mutual exclusion algorithms. Thus, comparison primitives may not be the best choice to provide in hardware if one is interested in scalable synchronization.

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Abstract. We propose a framework for reasoning about unbounded dynamic networks of infinite-state processes. We propose Constrained Petri Nets (CPN) as generic models for these networks. They can be seen as Petri nets where tokens (representing occurrences of processes) are colored by values over some potentially infinite data domain such as integers, reals, etc. Furthermore, we define a logic, called CML (colored markings logic), for the description of CPN configurations. CML is a first-order logic over tokens allowing to reason about their locations and their colors. Both CPNs and CML are parametrized by a color logic allowing to express constraints on the colors (data) associated with tokens. We investigate the decidability of the satisfiability problem of CML and its applications in the verification of CPNs. We identify a fragment of CML for which the satisfiability problem is decidable (whenever it is the case for the underlying color logic), and which is closed under the computations of post and pre images for CPNs. These results can be used for several kinds of analysis such as invariance checking, pre-post condition reasoning, and bounded reachability analysis. 1.

We present an N-process local-spin mutual exclusion algorithm, based on nonatomic reads and writes, in which each process performs \Theta (log N) remote memory references to enter and exit its critical section. This algorithm is derived from Yang and Anderson's atomic tree-based local-spin algorithm in a way that preserves its time complexity. No atomic read/write algorithm with better asymptotic worst-case time complexity (under the remote-memory-references measure) is currently known. This suggests that atomic memory is not fundamentally required if one is interested in worst-case time complexity. The same cannot be said if one is interested in fast-path algorithms (in which contention-free time complexity is required to be O(1)) or adaptive algorithms (in which time complexity is required to be proportional to the number of contending processes). We show that such algorithms fundamentally require memory accesses to be atomic. In particular, we show that for any N-process nonatomic algorithm, there exists a single-process execution in which the lone competing process executes \Omega (log N / log log N) remote operations to enter its critical section. Moreover, these operations must access \Omega (plog N / log log N) distinct variables, which implies that fast and adaptive algorithms are impossible even if caching techniques are used to avoid accessing the processors-to-memory interconnection network.

This dissertation is in two parts, covering two distinct areas of distributed computing. The first part concerns timing models in distributed systems that lie between the synchronous and asynchronous models in terms of their assumption on synchrony. We study their time complexity for solving distributed computing problems in shared memory (SM) and message-passing (MP) systems. We consider four timing parameters: the upper and lower bounds on process step time and message delay. Timing models are obtained by considering independently whether each parameter is known (i.e., is hard-wired into processes' code) or unknown, giving rise to four SM models and 16 MP models. We also study other timing models that are not covered by this framework. We show a general time complexity hierarchy indicating inherent time complexity gaps among the models. The time complexity gaps are introduced by the time complexity of the session problem, an abstraction of fundamental synchronization problems in dist...

In this paper we study the ability of shared object types to implement Consensus in asynchronous shared-memory systems where at most one process may crash. More specifically, we consider the following question: Let n 3 and S be a set of object types that can be used to solve one-resilient Consensus among n processes. Can S always be used to solve one-resilient Consensus among n \Gamma 1 processes? We prove that for n = 3 the answer is negative, even if S consists only of deterministic types. (This strengthens an earlier result by the first author proving the same fact for nondeterministic types.) We also prove that, in contrast, for n ? 3 the answer to the above question is affirmative.

This paper has explored three examples of good semantical analyses of programming structures. The three examples share two characteristics: the semantic models are abstract enough to be applicable in many situations, and the models lead to proofs of non-computability. Other examples of programming structures have been omitted from this short essay: foundations for object-oriented languages, descriptions of languages with local variables, and the theory of database query languages. Each of these examples have corresponding semantical theories that enjoy the two characteristics above. The richness of programming structure suggests a corollary: it is folly to look for one universal model to explain all programming structures. Of course, as a theoretical subject, semantics benefits from the reduction of many concepts to a primitive, common level. Nevertheless, reduction must often be resisted. We have seen how computability theory loses all kinds of relevant distinctions. Another example is the naive semantics of PCF based on dcpos: the model is not abstract enough,