Search for: All records

SIMD||DNA [Wang et al., 2019] is a model of DNA strand displacement allowing parallel in-memory computation on DNA storage. We show how to simulate an arbitrary 3-symbol space-bounded Turing machine with a SIMD||DNA program, giving a more direct and efficient route to general-purpose information manipulation on DNA storage than the Rule 110 simulation of Wang, Chalk, and Soloveichik [Wang et al., 2019]. We also develop software (https://github.com/UC-Davis-molecular-computing/simd-dna) that can simulate SIMD||DNA programs and produce SVG figures. 

The population protocol model describes a network of anonymous agents that interact asynchronously in pairs chosen at random. Each agent starts in the same initial state s. We introduce the *dynamic size counting* problem: approximately counting the number of agents in the presence of an adversary who at any time can remove any number of agents or add any number of new agents in state s. A valid solution requires that after each addition/removal event, resulting in population size n, with high probability each agent "quickly" computes the same constant-factor estimate of the value log2n (how quickly is called the *convergence* time), which remains the output of every agent for as long as possible (the *holding* time). Since the adversary can remove agents, the holding time is necessarily finite: even after the adversary stops altering the population, it is impossible to *stabilize* to an output that never again changes. We first show that a protocol solves the dynamic size counting problem if and only if it solves the *loosely-stabilizing counting* problem: that of estimating logn in a *fixed-size* population, but where the adversary can initialize each agent in an arbitrary state, with the same convergence time and holding time. We then show a protocol solving the loosely-stabilizing counting problem with the following guarantees: if the population size is n, M is the largest initial estimate of logn, and s is the maximum integer initially stored in any field of the agents' memory, we have expected convergence time O(logn+logM), expected polynomial holding time, and expected memory usage of O(log2(s)+(loglogn)2) bits. Interpreted as a dynamic size counting protocol, when changing from population size nprev to nnext, the convergence time is O(lognnext+loglognprev).