The Firing Squad Problem Revisited

In the classical firing squad problem, an unknown number of nodes represented by identical finite state machines is arranged on a line and in each time unit each node may change its state according to its neighbors\u27 states. Initially all nodes are passive, except one specific node located at an end of the line, which issues a fire command. This command needs to be propagated to all other nodes, so that eventually all nodes simultaneously enter some designated ``firing" state. A natural extension of the firing squad problem, introduced in this paper, allows each node to postpone its participation in the squad for an arbitrary time, possibly forever, and firing is allowed only after all nodes decided to participate. This variant is highly relevant in the context of decentralized distributed computing, where processes have to coordinate for initiating various tasks simultaneously. The main goal of this paper is to study the above variant of the firing squad problem under the assumptions that the nodes are infinite state machines, and that the inter-node communication links can be changed arbitrarily in each time unit, i.e., are defined by a dynamic graph. In this setting, we study the following fundamental question: what connectivity requirements enable a solution to the firing squad problem? Our main result is an exact characterization of the dynamic graphs for which the firing squad problem can be solved. When restricted to static directed graphs, this characterization implies that the problem can be solved if and only if the graph is strongly connected. We also discuss how information on the number of nodes or on the diameter of the network, and the use of randomization, can improve the solutions to the problem

Relating Knowledge and Coordinated Action: The Knowledge of Preconditions Principle

The Knowledge of Preconditions principle (KoP) is proposed as a widely applicable connection between knowledge and action in multi-agent systems. Roughly speaking, it asserts that if some condition is a necessary condition for performing a given action A, then knowing that this condition holds is also a necessary condition for performing A. Since the specifications of tasks often involve necessary conditions for actions, the KoP principle shows that such specifications induce knowledge preconditions for the actions. Distributed protocols or multi-agent plans that satisfy the specifications must ensure that this knowledge be attained, and that it is detected by the agents as a condition for action. The knowledge of preconditions principle is formalised in the runs and systems framework, and is proven to hold in a wide class of settings. Well-known connections between knowledge and coordinated action are extended and shown to derive directly from the KoP principle: a "common knowledge of preconditions" principle is established showing that common knowledge is a necessary condition for performing simultaneous actions, and a "nested knowledge of preconditions" principle is proven, showing that coordinating actions to be performed in linear temporal order requires a corresponding form of nested knowledge.Comment: In Proceedings TARK 2015, arXiv:1606.0729

From Individual to Collective Responsibility: There and Back Again

This chapter argues that in cases in which a (non-institutional) group is collectively causally responsible and collectively morally responsible for some harm which is either (i) brought about intentionally or (ii) foreseen as the side effect of something brought about intentionally or (iii) unforeseen but a nonaggregative harm, each member of the group is equally and as fully responsible for the harm as if he or she had done it alone

Kim on Causation and Mental Causation

Jaegwon Kim’s views on mental causation and the exclusion argument are evaluated systematically. Particular attention is paid to different theories of causation. It is argued that the exclusion argument and its premises do not cohere well with any systematic view of causation

Nothing Less Than the Dignity of Man: The Eighth Amendment and State Efforts to Reinstitute Traditional Methods of Execution

While lethal injection is the predominant method of executing death row inmates in America, European export bans and pharmaceutical manufacturers’ refusal to supply execution drugs has impeded the ability of states’ departments of corrections to obtain the drugs used for lethal injections. Facing a drug shortage, several death penalty states have considered legislation to reinstate the use of electric chairs, firing squads, and gas chambers. Efforts to restore traditional methods of capital punishment raise questions about whether such methods still comply with the Eighth Amendment’s prohibition against cruel and unusual punishments. The Supreme Court has observed that the Eighth Amendment is not static, but draws its meaning from society’s “evolving standards of decency.” To assess these evolving standards, the Court previously has looked to state laws to determine if a national consensus exists with respect to who is eligible for capital punishment and by what means states carry out death sentences. States have moved away from traditional methods of capital punishment. This trend suggests the traditional methods of capital punishment have fallen out of favor and can no longer withstand Eighth Amendment scrutiny

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

Killer Collapse: Empirically Probing the Philosophically Unsatisfactory Region of GRW

GRW theory offers precise laws for the collapse of the wave function. These collapses are characterized by two new constants, λ and σ. Recent work has put experimental upper bounds on the collapse rate, λ. Lower bounds on λ have been more controversial since GRW begins to take on a many-worlds character for small values of λ. Here I examine GRW in this odd region of parameter space where collapse events act as natural disasters that destroy branches of the wave function along with their occupants. Our continued survival provides evidence that we don't live in a universe like that. I offer a quantitative analysis of how such evidence can be used to assess versions of GRW with small collapse rates in an effort to move towards more principled and experimentally-informed lower bounds for λ

A Quantum Game of Life

This research describes a three dimensional quantum cellular automaton (QCA) which can simulate all other 3D QCA. This intrinsically universal QCA belongs to the simplest subclass of QCA: Partitioned QCA (PQCA). PQCA are QCA of a particular form, where incoming information is scattered by a fixed unitary U before being redistributed and rescattered. Our construction is minimal amongst PQCA, having block size 2 x 2 x 2 and cell dimension 2. Signals, wires and gates emerge in an elegant fashion.Comment: 13 pages, 10 figures. Final version, accepted by Journ\'ees Automates Cellulaires (JAC 2010)