scholarly journals A tight lower bound for semi-synchronous collaborative grid exploration

2020 ◽  
Vol 33 (6) ◽  
pp. 471-484
Author(s):  
Sebastian Brandt ◽  
Jara Uitto ◽  
Roger Wattenhofer
Keyword(s):  
Lower Bound ◽  
Finite Automaton ◽  
Finite Automata ◽  
Grid Cell ◽  
Grid Cells ◽  
Initial State ◽  
Selected Subset ◽  
Open Question ◽  
Agent Protocol

Abstract Recently, there has been a growing interest in grid exploration by agents with limited capabilities. We show that the grid cannot be explored by three semi-synchronous finite automata, answering an open question by Emek et al. (Theor Comput Sci 608:255–267, 2015) in the negative. In the setting we consider, time is divided into discrete steps, where in each step, an adversarially selected subset of the agents executes one look–compute–move cycle. The agents operate according to a shared finite automaton, where every agent is allowed to have a distinct initial state. The only means of communication is to sense the states of the agents sharing the same grid cell. The agents are equipped with a global compass and whenever an agent moves, the destination cell of the movement is chosen by the agent’s automaton from the set of neighboring grid cells. In contrast to the four agent protocol by Emek et al., we show that three agents do not suffice for grid exploration.

SIMULATIONS OF UNARY ONE-WAY MULTI-HEAD FINITE AUTOMATA

2014 ◽  
Vol 25 (07) ◽  
pp. 877-896 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER ◽  
MATTHIAS WENDLANDT
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Unary Languages ◽  
Order Of Magnitude ◽  
Simulation Results ◽  
Special Case ◽  
Nondeterministic Finite Automaton

We investigate the descriptional complexity of deterministic one-way multi-head finite automata accepting unary languages. It is known that in this case the languages accepted are regular. Thus, we study the increase of the number of states when an n-state k-head finite automaton is simulated by a classical (one-head) deterministic or nondeterministic finite automaton. In the former case upper and lower bounds that are tight in the order of magnitude are shown. For the latter case we obtain an upper bound of O(n2k) and a lower bound of Ω(nk) states. We investigate also the costs for the conversion of one-head nondeterministic finite automata to deterministic k-head finite automata, that is, we trade nondeterminism for heads. In addition, we study how the conversion costs vary in the special case of finite and, in particular, of singleton unary lanuages. Finally, as an application of the simulation results, we show that decidability problems for unary deterministic k-head finite automata such as emptiness or equivalence are LOGSPACE-complete.

On the Length of Shortest Strings Accepted by Two-way Finite Automata

2021 ◽  
Vol 180 (4) ◽  
pp. 315-331
Author(s):  
Egor Dobronravov ◽  
Nikita Dobronravov ◽  
Alexander Okhotin
Keyword(s):  
Lower Bound ◽  
Finite Automaton ◽  
Finite Automata ◽  
Deterministic Automata

Given a two-way finite automaton recognizing a non-empty language, consider the length of the shortest string it accepts, and, for each n ≥ 1, let f(n) be the maximum of these lengths over all n-state automata. It is proved that for n-state two-way finite automata, whether deterministic or nondeterministic, this number is at least Ω(10n/5) and less than (2nn+1), with the lower bound reached over an alphabet of size Θ(n). Furthermore, for deterministic automata and for a fixed alphabet of size m ≥ 1, the length of the shortest string is at least e(1+o(1))mn(log n− log m).

A Model of Secure Functioning of Computer Systems

2021 ◽  
Vol 12 (3) ◽  
pp. 150-156
Author(s):  
A. V. Galatenko ◽  
◽  
V. A. Kuzovikhina ◽  
Keyword(s):  
Lower Bound ◽  
Computer System ◽  
Finite Automaton ◽  
Nonnegative Integer ◽  
The Other ◽  
Shannon Function ◽  
Security Breaches ◽  
System Functioning ◽  
The Cost ◽  
The Given

We propose an automata model of computer system security. A system is represented by a finite automaton with states partitioned into two subsets: "secure" and "insecure". System functioning is secure if the number of consecutive insecure states is not greater than some nonnegative integer k. This definition allows one to formally reflect responsiveness to security breaches. The number of all input sequences that preserve security for the given value of k is referred to as a k-secure language. We prove that if a language is k-secure for some natural and automaton V, then it is also k-secure for any 0 < k < k and some automaton V = V (k). Reduction of the value of k is performed at the cost of amplification of the number of states. On the other hand, for any non-negative integer k there exists a k-secure language that is not k"-secure for any natural k" > k. The problem of reconstruction of a k-secure language using a conditional experiment is split into two subcases. If the cardinality of an input alphabet is bound by some constant, then the order of Shannon function of experiment complexity is the same for al k; otherwise there emerges a lower bound of the order nk.

scholarly journals Description and Analysis of a 20-Year (1960-79) Digital Ice-Concentration Database for the Great Lakes of North America

1983 ◽  
Vol 4 ◽  
pp. 14-18 ◽  
Author(s):  
Raymond A. Assel
Keyword(s):  
North America ◽  
Great Lakes ◽  
Surface Area ◽  
Information Service ◽  
Grid Cell ◽  
Ice Cover ◽  
Unit Surface Area ◽  
Grid Cells ◽  
Data Set ◽  
Ice Concentration

A digital ice-concentration database spanning 20 years (1960 to 1979) was established for the Great Lakes of North America. Data on ice concentration, i.e. the percentage of a unit surface area of the lake that is ice-covered, were abstracted from over 2 800 historic ice charts produced by United States and Canadian government agencies. The database consists of ice concentrations ranging from zero to 100% in 10% increments for individual grid cells of size 5 × 5 km constituting the surface area of each Great Lake. The data set for each of the Great Lakes was divided into half-month periods for statistical analysis. Maxinium, minimum, median, mode, and average ice-concentrations statistics were calculated for each grid cell and half-month period. A lakewide average value was then calculated for each of the half-month ice-concentration statistics for all grid cells for a given lake. Ice-cover variability and the normal extent and progression of the ice cover is discussed within the context of the lakewide averaged value of the minimum and maximum ice concentrations and the lakewide averaged value of the median ice concentrations, respectively. Differences in ice-cover variability among the five Great Lakes are related to mean lake depth and accumulated freezing degree-days. A Great Lakes ice atlas presenting a series of ice charts which depict the maximum, minimum, and median icecover concentrations for each of the Great Lakes for nine half-monthly periods, starting the last half of December and continuing through the last half of April will be published in 1983 by the National Oceanic and Atmospheric Administration (NOAA). The database will be archived at the National Snow and Ice Data Center of the National Environmental Satellite Data and Information Service (NESDIS) in Boulder, Colorado, USA, also in 1983.

scholarly journals A new discrete multiplicative random cascade model for downscaling intermittent rainfall fields

2019 ◽  
Author(s):  
Marc Schleiss
Keyword(s):  
Classical Method ◽  
Mathematical Problem ◽  
Grid Cell ◽  
Cascade Model ◽  
Small Scale ◽  
Grid Cells ◽  
Cascade Generator ◽  
Cascade Models ◽  
First Results ◽  
Original Amount

Abstract. Spatial downscaling of rainfall fields is a challenging mathematical problem for which many different types of methods have been proposed. One popular solution consists in redistributing rainfall amounts over smaller and smaller scales by means of a discrete multiplicative random cascade (DMRC). This works well for slowly varying, homogeneous rainfall fields but often fails in the presence of intermittency (i.e., large amounts of zero rainfall values). The most common workaround in this case is to use two separate cascade models, one for the occurrence and another for the intensity. In this paper, a new and simpler approach based on the notion of equal-volume areas (EVAs) is proposed. Unlike classical cascades where rainfall amounts are redistributed over grid cells of equal size, the EVA cascade splits grid cells into areas of different sizes, each of them containing exactly half of the original amount of water. The relative areas of the sub-grid cells are determined by drawing random values from a logit-normal cascade generator model with scale and intensity dependent standard deviation. The process ends when the amount of water in each sub-grid cell is smaller than a fixed bucket capacity, at which point the output of the cascade can be re-sampled over a regular Cartesian mesh. The present paper describes the implementation of the EVA cascade model and gives some first results for 100 selected events in the Netherlands. Performance is assessed by comparing the outputs of the EVA model to bilinear interpolation and to a classical DMRC model based on fixed grid cell sizes. Results show that on average, the EVA cascade outperforms the classical method, producing fields with more realistic distributions, small-scale extremes and spatial structures. Improvements are mostly credited to the higher robustness of the EVA model to the presence of intermittency and to the lower variance of its generator. However, improvements are not systematic and both approaches have their advantages and weaknesses. For example, while the classical cascade tends to overestimate small-scale extremes and variability, the EVA model tends to produce fields that are slightly too smooth and blocky compared with observations.

scholarly journals Neurobiological successor features for spatial navigation

2019 ◽  
Author(s):  
William de Cothi ◽  
Caswell Barry
Keyword(s):  
Grid Cell ◽  
Biological Data ◽  
Basis Set ◽  
Grid Cells ◽  
Dimensional Representation ◽  
Boundary Vector ◽  
Good Account ◽  
Cell Firing ◽  
Low Dimensional ◽  
Environmental Geometry

AbstractThe hippocampus has long been observed to encode a representation of an animal’s position in space. Recent evidence suggests that the nature of this representation is somewhat predictive and can be modelled by learning a successor representation (SR) between distinct positions in an environment. However, this discretisation of space is subjective making it difficult to formulate predictions about how some environmental manipulations should impact the hippocampal representation. Here we present a model of place and grid cell firing as a consequence of learning a SR from a basis set of known neurobiological features – boundary vector cells (BVCs). The model describes place cell firing as the successor features of the SR, with grid cells forming a low-dimensional representation of these successor features. We show that the place and grid cells generated using the BVC-SR model provide a good account of biological data for a variety of environmental manipulations, including dimensional stretches, barrier insertions, and the influence of environmental geometry on the hippocampal representation of space.

scholarly journals State Complexity of Neighbourhoods and Approximate Pattern Matching

2018 ◽  
Vol 29 (02) ◽  
pp. 315-329 ◽  
Author(s):  
Timothy Ng ◽  
David Rappaport ◽  
Kai Salomaa
Keyword(s):  
Lower Bound ◽  
Pattern Matching ◽  
Finite Automaton ◽  
The State ◽  
Worst Case ◽  
State Complexity ◽  
Approximate Pattern Matching ◽  
The Given ◽  
Nondeterministic Finite Automaton ◽  
Distance Formula

The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].

scholarly journals Path integration in place cells of developing rats

2018 ◽  
Vol 115 (7) ◽  
pp. E1637-E1646 ◽  
Author(s):  
Tale L. Bjerknes ◽  
Nenitha C. Dagslott ◽  
Edvard I. Moser ◽  
May-Britt Moser
Keyword(s):  
Path Integration ◽  
Grid Cell ◽  
Cell System ◽  
Place Cells ◽  
Postnatal Life ◽  
Motion Information ◽  
Grid Cells ◽  
Adult Rats ◽  
Self Motion ◽  
Made In

Place cells in the hippocampus and grid cells in the medial entorhinal cortex rely on self-motion information and path integration for spatially confined firing. Place cells can be observed in young rats as soon as they leave their nest at around 2.5 wk of postnatal life. In contrast, the regularly spaced firing of grid cells develops only after weaning, during the fourth week. In the present study, we sought to determine whether place cells are able to integrate self-motion information before maturation of the grid-cell system. Place cells were recorded on a 200-cm linear track while preweaning, postweaning, and adult rats ran on successive trials from a start wall to a box at the end of a linear track. The position of the start wall was altered in the middle of the trial sequence. When recordings were made in complete darkness, place cells maintained fields at a fixed distance from the start wall regardless of the age of the animal. When lights were on, place fields were determined primarily by external landmarks, except at the very beginning of the track. This shift was observed in both young and adult animals. The results suggest that preweaning rats are able to calculate distances based on information from self-motion before the grid-cell system has matured to its full extent.

Lower Bounds on OBDD Proofs with Several Orders

2021 ◽  
Vol 22 (4) ◽  
pp. 1-30
Author(s):  
Sam Buss ◽  
Dmitry Itsykson ◽  
Alexander Knop ◽  
Artur Riazanov ◽  
Dmitry Sokolov
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Communication Complexity ◽  
Multiparty Communication ◽  
Constant Degree ◽  
Polynomial Size ◽  
Explicit Constant ◽  
Open Question ◽  
System 1 ◽  
Exponential Size

This article is motivated by seeking lower bounds on OBDD(∧, w, r) refutations, namely, OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1 - NBP ∧ refutations based on read-once nondeterministic branching programs. These generalize OBDD(∧, r) refutations. There are polynomial size 1 - NBP(∧) refutations of the pigeonhole principle, hence 1-NBP(∧) is strictly stronger than OBDD}(∧, r). There are also formulas that have polynomial size tree-like resolution refutations but require exponential size 1-NBP(∧) refutations. As a corollary, OBDD}(∧, r) does not simulate tree-like resolution, answering a previously open question. The system 1-NBP(∧, ∃) uses projection inferences instead of weakening. 1-NBP(∧, ∃ k is the system restricted to projection on at most k distinct variables. We construct explicit constant degree graphs G n on n vertices and an ε > 0, such that 1-NBP(∧, ∃ ε n ) refutations of the Tseitin formula for G n require exponential size. Second, we study the proof system OBDD}(∧, w, r ℓ ), which allows ℓ different variable orders in a refutation. We prove an exponential lower bound on the complexity of tree-like OBDD(∧, w, r ℓ ) refutations for ℓ = ε log n , where n is the number of variables and ε > 0 is a constant. The lower bound is based on multiparty communication complexity.

Grid Cells Lose Coherence in Realistic Environments

2021 ◽  
Author(s):  
Yifan Luo ◽  
Matteo Toso ◽  
Bailu Si ◽  
Federico Stella ◽  
Alessandro Treves
Keyword(s):  
Short Range ◽  
Short Range Order ◽  
Grid Cell ◽  
Place Cells ◽  
Grid Cells ◽  
Lateral Connectivity ◽  
Cell Pattern ◽  
In The Wild ◽  
Freely Moving ◽  
Adaptation Model

Spatial cognition in naturalistic environments, for freely moving animals, may pose quite different constraints from that studied in artificial laboratory settings. Hippocampal place cells indeed look quite different, but almost nothing is known about entorhinal cortex grid cells, in the wild. Simulating our self-organizing adaptation model of grid cell pattern formation, we consider a virtual rat randomly exploring a virtual burrow, with feedforward connectivity from place to grid units and recurrent connectivity between grid units. The virtual burrow was based on those observed by John B. Calhoun, including several chambers and tunnels. Our results indicate that lateral connectivity between grid units may enhance their “gridness” within a limited strength range, but the overall effect of the irregular geometry is to disable long-range and obstruct short-range order. What appears as a smooth continuous attractor in a flat box, kept rigid by recurrent connections, turns into an incoherent motley of unit clusters, flexible or outright unstable.

Sign in / Sign up

Export Citation Format

Share Document