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We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the…
We prove that a random automaton with $n$ states and any fixed non-singleton alphabet is synchronizing with high probability (modulo an unpublished result about unique highest trees of random graphs). Moreover, we also prove that the…
We consider the configuration formation problem in modular robotic systems where a set of singleton modules that are spatially distributed in an environment are required to assume appropriate positions so that they can configure into a new,…
In several social choice problems, agents collectively make decisions over the allocation of multiple divisible and heterogeneous resources with capacity constraints to maximize utilitarian social welfare. The agents are constrained through…
This work studies consensus strategies for networks of agents with limited memory, computation, and communication capabilities. We assume that agents can process only values from a finite alphabet, and we adopt the framework of finite…
Grover's quantum algorithm for an unstructured search problem and the Count algorithm by Brassard et al. are generalized to the case when the initial state is arbitrarily and maximally entangled. This ansatz might be relevant with quantum…
Information gathered along a path is inherently submodular; the incremental amount of information gained along a path decreases due to redundant observations. In addition to submodularity, the incremental amount of information gained is a…
The Turing Machine has two implicit properties that depend on its underlying notion of computing: the format is fully determinate and computations are information preserving. Distributed representations lack these properties and cannot be…
We introduce the concept of knowledge states; many well-known algorithms can be viewed as knowledge state algorithms. The knowledge state approach can be used to to construct competitive randomized online algorithms and study the tradeoff…
We consider a model where an agent has a repeated decision to make and wishes to maximize their total payoff. Payoffs are influenced by an action taken by the agent, but also an unknown state of the world that evolves over time. Before…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
Motivated by earlier results on universal randomized guessing, we consider an individual-sequence approach to the guessing problem: in this setting, the goal is to guess a secret, individual (deterministic) vector $x^n=(x_1,\ldots,x_n)$, by…
The basis for most of the ideas mentioned in this paper is the theory of cellular automata. A cellular automata contains a regular grid of cells, with each cell having a pre-defined set of finite states. The initial state is determined at…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
We consider the problem of designing agents able to compute optimal decisions by composing data from multiple sources to tackle tasks involving: (i) tracking a desired behavior while minimizing an agent-specific cost; (ii) satisfying safety…
We present a few results and several open problems concerning complete deterministic finite automata in which every non-empty subset of the state set occurs as the image of the whole state set under the action of a suitable input word.
The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…
We consider a social system of interacting heterogeneous agents with learning abilities, a model close to Random Field Ising Models, where the random field corresponds to the idiosyncratic willingness to pay. Given a fixed price, agents…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…