Related papers: Succinct Population Protocols for Presburger Arith…
In this paper, we continue a line of work on obtaining succinct population protocols for Presburger-definable predicates. More specifically, we focus on threshold predicates. These are predicates of the form $n\ge d$, where $n$ is a free…
Population protocols are a model of distributed computation in which an arbitrary number of indistinguishable finite-state agents interact in pairs to decide some property of their initial configuration. We investigate the behaviour of…
We study population protocols: networks of anonymous agents that interact under a scheduler that picks pairs of agents uniformly at random. The _size counting problem_ is that of calculating the exact number $n$ of agents in the population,…
We propose $\omega$MSO$\Join$BAPA, an expressive logic for describing countable structures, which subsumes and transcends both Counting Monadic Second-Order Logic (CMSO) and Boolean Algebra with Presburger Arithmetic (BAPA). We show that…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
Population protocols [Angluin et al., PODC, 2004] are a model of distributed computation in which indistinguishable, finite-state agents interact in pairs to decide if their initial configuration, i.e., the initial number of agents in each…
Population protocols are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated…
We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are…
Population protocols are a formal model of computation by identical, anonymous mobile agents interacting in pairs. Their computational power is rather limited: Angluin et al. have shown that they can only compute the predicates over…
Population protocols have been introduced by Angluin et al. as a model of networks consisting of very limited mobile agents that interact in pairs but with no control over their own movement. A collection of anonymous agents, modeled by…
Population protocols (Angluin et al., PODC, 2004) are a formal model of sensor networks consisting of identical mobile devices. Two devices can interact and thereby change their states. Computations are infinite sequences of interactions…
A population protocol can be viewed as a sequence of pairwise interactions of $n$ agents (nodes). During one interaction, two agents selected uniformly at random update their states by applying a specified deterministic transition function.…
Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii)…
This paper studies what can be computed by using probabilistic local interactions with agents with a very restricted power in polylogarithmic parallel time. It is known that if agents are only finite state (corresponding to the Population…
Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
Population protocols are a relatively novel computational model in which very resource-limited anonymous agents interact in pairs with the goal of computing predicates. We consider the probabilistic version of this model, which naturally…
In this work, we initiate the study of \emph{smoothed analysis} of population protocols. We consider a population protocol model where an adaptive adversary dictates the interactions between agents, but with probability $p$ every such…
Population protocols are networks of finite-state agents, interacting randomly, and updating their states using simple rules. Despite their extreme simplicity, these systems have been shown to cooperatively perform complex computational…
We investigate expansions of Presburger arithmetic, i.e., the theory of the integers with addition and order, with additional structure related to exponentiation: either a function that takes a number to the power of $2$, or a predicate for…