3,317 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Minimum algorithm sizes for self-stabilizing gathering and related problems of autonomous mobile robots
We investigate a swarm of autonomous mobile robots in the Euclidean plane. A
robot has a function called {\em target function} to determine the destination
point from the robots' positions. All robots in the swarm conventionally take
the same target function, but there is apparent limitation in problem-solving
ability. We allow the robots to take different target functions. The number of
different target functions necessary and sufficient to solve a problem is
called the {\em minimum algorithm size} (MAS) for . We establish the MASs
for solving the gathering and related problems from {\bf any} initial
configuration, i.e., in a {\bf self-stabilizing} manner. We show, for example,
for , there is a problem such that the MAS for the
is , where is the size of swarm. The MAS for the gathering
problem is 2, and the MAS for the fault tolerant gathering problem is 3, when
robots may crash, but the MAS for the problem of gathering all
robot (including faulty ones) at a point is not solvable (even if all robots
have distinct target functions), as long as a robot may crash
Semi-simplicial Set Models for Distributed Knowledge
In recent years, a new class of models for multi-agent epistemic logic has
emerged, based on simplicial complexes. Since then, many variants of these
simplicial models have been investigated, giving rise to different logics and
axiomatizations.
In this paper, we present a further generalization, where a group of agents
may distinguish two worlds, even though each individual agent in the group is
unable to distinguish them. For that purpose, we generalize beyond simplicial
complexes and consider instead simplicial sets. By doing so, we define a new
semantics for epistemic logic with distributed knowledge. As it turns out,
these models are the geometric counterpart of a generalization of Kripke
models, called "pseudo-models". We identify various interesting sub-classes of
these models, encompassing all previously studied variants of simplicial
models; and give a sound and complete axiomatization for each of them
Making Self-Stabilizing Algorithms for Any Locally Greedy Problem
Self-stabilizing algorithms are a way to deal with network dynamicity, as it will update itself after a network change (addition or removal of nodes or edges), as long as changes are not frequent. We propose an automatic transformation of synchronous distributed algorithms that solve locally greedy and mendable problems into self-stabilizing algorithms in anonymous networks.
Mendable problems are a generalization of greedy problems where any partial solution may be transformed -instead of completed- into a global solution: every time we extend the partial solution, we are allowed to change the previous partial solution up to a given distance. Locally here means that to extend a solution for a node, we need to look at a constant distance from it.
In order to do this, we propose the first explicit self-stabilizing algorithm computing a (k,k-1)-ruling set (i.e. a "maximal independent set at distance k"). By combining this technique multiple times, we compute a distance-K coloring of the graph. With this coloring we can finally simulate Local model algorithms running in a constant number of rounds, using the colors as unique identifiers.
Our algorithms work under the Gouda daemon, similar to the probabilistic daemon: if an event should eventually happen, it will occur
Parameterized Complexity of Binary CSP: Vertex Cover, Treedepth, and Related Parameters
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:
- Binary CSP parameterized by the vertex cover number is W[3]-complete. More generally, for every positive integer d, Binary CSP parameterized by the size of a modulator to a treedepth-d graph is W[2d+1]-complete. This provides a new family of natural problems that are complete for odd levels of the W-hierarchy.
- We introduce a new complexity class XSLP, defined so that Binary CSP parameterized by treedepth is complete for this class. We provide two equivalent characterizations of XSLP: the first one relates XSLP to a model of an alternating Turing machine with certain restrictions on conondeterminism and space complexity, while the second one links XSLP to the problem of model-checking first-order logic with suitably restricted universal quantification. Interestingly, the proof of the machine characterization of XSLP uses the concept of universal trees, which are prominently featured in the recent work on parity games.
- We describe a new complexity hierarchy sandwiched between the W-hierarchy and the A-hierarchy: For every odd t, we introduce a parameterized complexity class S[t] with W[t] ? S[t] ? A[t], defined using a parameter that interpolates between the vertex cover number and the treedepth. We expect that many of the studied classes will be useful in the future for pinpointing the complexity of various structural parameterizations of graph problems
Functional completeness of planar Rydberg blockade structures
The construction of Hilbert spaces that are characterized by local
constraints as the low-energy sectors of microscopic models is an important
step towards the realization of a wide range of quantum phases with long-range
entanglement and emergent gauge fields. Here we show that planar structures of
trapped atoms in the Rydberg blockade regime are functionally complete: Their
ground state manifold can realize any Hilbert space that can be characterized
by local constraints in the product basis. We introduce a versatile framework,
together with a set of provably minimal logic primitives as building blocks, to
implement these constraints. As examples, we present lattice realizations of
the string-net Hilbert spaces that underlie the surface code and the Fibonacci
anyon model. We discuss possible optimizations of planar Rydberg structures to
increase their geometrical robustness.Comment: 33 pages, 14 figures, v2: fixed typos, added additional references
and comment
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