Joseph Y. Halpern

“Sometimes” and “not never” revisited: on branching versus linear time temporal logic

The differences between and appropriateness of branching versus linear time temporal logic for reasoning about concurrent programs are studied. These issues have been previously considered by Lamport. To facilitate a careful examination of these issues, a language, CTL*, in which a universal or existential path quantifier can prefix an arbitrary linear time assertion, is defined. The expressive power of a number of sublanguages is then compared. CTL* is also related to the logics MPL of Abrahamson and PL of Harel, Kozen, and Parikh. The paper concludes with a comparison of the utility of branching and linear time temporal logics.

A guide to completeness and complexity for modal logics of knowledge and belief

Abstract We review and re-examine possible-worlds semantics for propositional logics of knowledge and belief with three particular points of emphasis: (1) we show how general techniques for finding decision procedures and complete axiomatizations apply to models for knowledge and belief, (2) we show how sensitive the difficulty of the decision procedure is to such issues as the choice of modal operators and the axiom system, and (3) we discuss how notions of common knowledge and distributed knowledge among a group of agents fit into the possible-worlds framework, As far as complexity is concerned, we show, among other results, that while the problem of deciding satisfiability of an S5 formula with one agent is NP-complete, the problem for many agents is PSPACE-complete. Adding a distributed knowledge operator does not change the complexity, but once a common knowledge operator is added to the language, the problem becomes complete for exponential time.

Gossip-based ad hoc routing

Many ad hoc routing protocols are based on some variant of flooding. Despite various optimizations of flooding, many routing messages are propagated unnecessarily. We propose a gossiping-based approach, where each node forwards a message with some probability, to reduce the overhead of the routing protocols. Gossiping exhibits bimodal behavior in sufficiently large networks: in some executions, the gossip dies out quickly and hardly any node gets the message; in the remaining executions, a substantial fraction of the nodes gets the message. The fraction of executions in which most nodes get the message depends on the gossiping probability and the topology of the network. In the networks we have considered, using gossiping probability between 0.6 and 0.8 suffices to ensure that almost every node gets the message in almost every execution. For large networks, this simple gossiping protocol uses up to 35% fewer messages than flooding, with improved performance. Gossiping can also be combined with various optimizations of flooding to yield further benefits. Simulations show that adding gossiping to AODV results in significant performance improvement, even in networks as small as 150 nodes. Our results suggest that the improvement should be even more significant in larger networks

Analysis of a cone-based distributed topology control algorithm for wireless multi-hop networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology control algorithm. This algorithm, introduced in [16], does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node <i>u</i> transmits with the minimum power <i>p<subscrpt>u, α</subscrpt></i> required to ensure that in every cone of degree α around <i>u</i>, there is some node that <i>u</i> can reach with power <i>p<subscrpt>u, α</subscrpt></i>. We show that taking α = 5π/6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from <i>s</i> to <i>t</i> when every node communicates at maximum power then, if α ⪇ 5π/6, there is still a path in the smallest symmetric graph <i>G</i><subscrpt>α</subscrpt> containing all edges (<i>u, v</i>) such that <i>u</i> can communicate with <i>v</i> using power <i>p<subscrpt>u, α</subscrpt></i>. On the other hand, if α > 5π/6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.

Minimum-energy mobile wireless networks revisited

We propose a protocol that, given a communication network, computes a subnetwork such that, for every pair (u, /spl upsi/) of nodes connected in the original network, there is a a minimum-energy path between u and /spl upsi/ in the subnetwork (where a minimum-energy path is one that allows messages to be transmitted with a minimum use of energy). The network computed by our protocol is in general a subnetwork of the one computed by the protocol given by Rodoplu and Meng (see IEEE J. Selected Areas in Communications, vol.17, no.8, p.1333-44, 1999). Moreover, our protocol is computationally simpler. We demonstrate the performance improvements obtained by using the subnetwork computed by our protocol through simulation.

A propositional modal logic of time intervals

In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end, a modal temporal loglc based on time intervals is developed, a logic that can be viewed as a generalization of point-based modal temporal logic. Related loglcs are discussed, an intuitive presentation of the new logic is given, and its formal syntax and semantics are defined. No assumption is made about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals), or not (such as the rational). It is shown, however, that there are formulas in the logic that allow us to distinguish all these situations. A translation of our logic into first-order logic is given, which allows the application of some results on first-order logic to our modal logic. Finally. the difficulty of validity problems for the logic is considered. This turns out to depend critically, and in surprising ways, on our assumptions about time. For example, if our underlying temporal structure is the ratlonals, then, the validity problem is r. e .-complete; if it is the reals, then validity n II ~-hard: and if it is the natural numbers, then validity is fI ] -complete.

Causes and Explanations: A Structural-Model Approach. Part I: Causes

We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account. 1. Introduction2. Causal models: a review 2.1Causal models 2.2Syntax and semantics3. The definition of cause4. Examples5. A more refined definition6. Discussion AAppendix: Some Technical Issues A.1The active causal process A.2A closer look at AC2(b) A.3Causality with infinitely many variables A.4Causality in nonrecursive models Introduction Causal models: a review 2.1Causal models 2.2Syntax and semantics 2.1Causal models 2.2Syntax and semantics The definition of cause Examples A more refined definition Discussion AAppendix: Some Technical Issues A.1The active causal process A.2A closer look at AC2(b) A.3Causality with infinitely many variables A.4Causality in nonrecursive models

A cone-based distributed topology-control algorithm for wireless multi-hop networks

The topology of a wireless multi-hop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a cone-based distributed topology-control (CBTC) algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p/sub u,/spl alpha// required to ensure that in every cone of degree /spl alpha/ around u, there is some node that u can reach with power p/sub u,/spl alpha//. We show that taking /spl alpha/=5/spl pi//6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if /spl alpha//spl les/5/spl pi//6, there is still a path in the smallest symmetric graph G/sub /spl alpha// containing all edges (u,v) such that u can communicate with v using power p/sub u,/spl alpha//. On the other hand, if /spl alpha/>5/spl pi//6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations.

Rational secret sharing and multiparty computation: extended abstract

We consider the problems of secret sharing and multiparty computation, assuming that agents prefer to get the secret (resp., function value) to not getting it, and secondarily, prefer that as few as possible of the other agents get it. We show that, under these assumptions, neither secret sharing nor multiparty function computation is possible using a mechanism that has a fixed running time. However, we show that both are possible using randomized mechanisms with constant expected running time.

Knowledge and common knowledge in a distributed environment

We argue that the right way to understand distributed protocols is by considering how messages change the state of knowledge of a system. We present a hierarchy of knowledge states that a system may be in, and discuss how communication can move the systems state of knowledge of a fact up the hierarchy. Of special interest is the notion of common knowledge. Common knowledge is an essential state of knowledge for reaching agreements and coordinating action. We show that in practical distributed systems, common knowledge is not attainable. We introduce various relaxations of common knowledge that are attainable in many cases of interest. We describe in what sense these notions are appropriate, and discuss their relationship to each other. We conclude with a discussion of the role of knowledge in distributed systems.