Nondeterministic Time Research Articles

On the Consistency of Circuit Lower Bounds for Non-Deterministic Time

On the Consistency of Circuit Lower Bounds for Non-Deterministic Time

Expected Values in Complex Networks Constructed Using a Compression Algorithm to Time Series

This paper introduces a methodology for computing expected values associated with compression networks resulting from the application of compression algorithms to independent and identically distributed random time series. Our analysis establishes a robust correspondence between the calculated expected values and empirically derived results obtained from constructing networks using nondeterministic time series. Notably, the ratio of the average indegree of a network to the computed expected indegree for stochastic time series serves as a versatile metric. It enables the assessment of inherent randomness in time series and facilitates the distinction between nondeterministic and chaotic systems. The metric demonstrates high sensitivity to nondeterminism in both synthetic and real-world datasets, highlighting its capacity to detect subtle disturbances and high-frequency noise, even in series characterized by a deficient sample rate. Our results extend and confirm previous findings in the field.

Realizing Strong Determinism Contract on Log-Structured Merge Key-Value Stores

We propose Vigil-KV , a hardware and software co-designed framework that eliminates long-tail latency almost perfectly by introducing strong latency determinism. To make Get latency deterministic, Vigil-KV first enables a predictable latency mode (PLM) interface on a real datacenter-scale NVMe SSD, having knowledge about the nature of the underlying flash technologies. Vigil-KV at the system-level then hides the non-deterministic time window (associated with SSD’s internal tasks and/or write services) by internally scheduling the different device states of PLM across multiple physical functions. Vigil-KV further schedules compaction/flush operations and client requests being aware of PLM’s restrictions thereby integrating strong latency determinism into LSM KVs. We implement Vigil-KV upon a 1.92TB NVMe SSD prototype and Linux 4.19.91, but other LSM KVs can adopt its concept. We evaluate diverse Facebook and Yahoo scenarios with Vigil-KV, and the results show that Vigil-KV can reducethe tail latency of a baseline KV system by 3.19× while reducing the average latency by 34%, on average.

Improved Merlin–Arthur Protocols for Central Problems in Fine-Grained Complexity

In a Merlin–Arthur proof system, the proof verifier (Arthur) accepts valid proofs (from Merlin) with probability 1, and rejects invalid proofs with probability arbitrarily close to 1. The running time of such a system is defined to be the length of Merlin’s proof plus the running time of Arthur. We provide new Merlin–Arthur proof systems for some key problems in fine-grained complexity. In several cases our proof systems have optimal running time. Our main results include:Certifying that a list of n integers has no 3-SUM solution can be done in Merlin–Arthur time tilde{O}(n). Previously, Carmosino et al. [ITCS 2016] showed that the problem has a nondeterministic algorithm running in tilde{O}(n^{1.5}) time (that is, there is a proof system with proofs of length tilde{O}(n^{1.5}) and a deterministic verifier running in tilde{O}(n^{1.5}) time).Counting the number of k-cliques with total edge weight equal to zero in an n-node graph can be done in Merlin–Arthur time {tilde{O}}(n^{lceil k/2rceil }) (where kge 3). For odd k, this bound can be further improved for sparse graphs: for example, counting the number of zero-weight triangles in an m-edge graph can be done in Merlin–Arthur time {tilde{O}}(m). Previous Merlin–Arthur protocols by Williams [CCC’16] and Björklund and Kaski [PODC’16] could only count k-cliques in unweighted graphs, and had worse running times for small k.Computing the All-Pairs Shortest Distances matrix for an n-node graph can be done in Merlin–Arthur time tilde{O}(n^2). Note this is optimal, as the matrix can have Omega (n^2) nonzero entries in general. Previously, Carmosino et al. [ITCS 2016] showed that this problem has an tilde{O}(n^{2.94}) nondeterministic time algorithm.Certifying that an n-variable k-CNF is unsatisfiable can be done in Merlin–Arthur time 2^{n/2 - n/O(k)}. We also observe an algebrization barrier for the previous 2^{n/2}cdot textrm{poly}(n)-time Merlin–Arthur protocol of R. Williams [CCC’16] for #SAT: in particular, his protocol algebrizes, and we observe there is no algebrizing protocol for k-UNSAT running in 2^{n/2}/n^{omega (1)} time. Therefore we have to exploit non-algebrizing properties to obtain our new protocol.Certifying a Quantified Boolean Formula is true can be done in Merlin–Arthur time 2^{4n/5}cdot textrm{poly}(n). Previously, the only nontrivial result known along these lines was an Arthur–Merlin–Arthur protocol (where Merlin’s proof depends on some of Arthur’s coins) running in 2^{2n/3}cdot textrm{poly}(n) time. Due to the centrality of these problems in fine-grained complexity, our results have consequences for many other problems of interest. For example, our work implies that certifying there is no Subset Sum solution to n integers can be done in Merlin–Arthur time 2^{n/3}cdot textrm{poly}(n), improving on the previous best protocol by Nederlof [IPL 2017] which took 2^{0.49991n}cdot textrm{poly}(n) time.

Special Section on the Fifty-Second Annual ACM Symposium on the Theory of Computing (STOC 2020)

This issue of SICOMP contains six specially selected papers from STOC 2020, the Fifty-second Annual ACM Symposium on the Theory of Computing, which was held June 22--26, 2020, initially planned at Chicago, Illinois, but due to COVID-19 was an online conference in the end. The papers here were chosen to represent the range and quality of the STOC program. These papers have been revised and extended by their authors and subjected to the standard thorough reviewing process of SICOMP. The program committee for STOC 2020 consisted of an executive committee made up of Nima Anari, Boaz Barak, Sébastien Bubeck, Mark Bun, Arkadev Chattopadhyay, Chandra Chekuri, Julia Chuzhoy, Marek Cygan, Ilias Diakonikolas, Yevgeniy Dodis, Sebastian Forster, Ankit Garg, Nika Haghtalab, Prahladh Harsha, Justin Holmgren, Piotr Indyk, Rahul Jain, Sanjeev Khanna, Dakshita Khurana, Pravesh Kothari, Robert Krauthgamer, Marvin Künnemann, Tengyu Ma, Rafael Oliveira, Merav Parter, Sofya Raskhodnikova, Robert Robere, Dana Ron, Noga Ron-Zewi, Thatchaphol Saranurak, Balasubramanian Sivan, Christian Sohler, Madhur Tulsiani, Omri Weinstein, Christian Wulff-Nilsen, and Henry Yuen. The program chair was Julia Chuzhoy. Included in this issue are the following papers: ``Explicit Near-Ramanujan Graphs of Every Degree" by Sidhanth Mohanty, Ryan O'Donnell, and Pedro Paredes shows a deterministic poly$(n)$-time algorithm that outputs a $d$-regular graph on $\Theta(n)$ vertices that is $\epsilon$-near-Ramanujan. ``Reducing Path TSP to TSP" by Vera Traub, Jens Vygen, and Rico Zenklusen presents a black-box reduction from the path version of the traveling salesman problem (Path TSP) to the classical tour version (TSP). ``Nearly Optimal Static Las Vegas Succinct Dictionary" by Huacheng Yu obtains a randomized dictionary data structure using ${OPT}+{poly}\lg n+O(\lg^{(\ell)} U)$ bits of space with expected constant query time for the static dictionary problem. ``Separating the Communication Complexity of Truthful and Nontruthful Algorithms for Combinatorial Auctions" by Sepehr Assadi, Hrishikesh Khandeparkar, Raghuvansh Raj Saxena, and S. Matthew Weinberg provides the first separation in the approximation guarantee achievable by truthful and nontruthful combinatorial auctions with polynomial communication. ``Strong Average-Case Circuit Lower Bounds from Nontrivial Derandomization" by Lijie Chen and Hanlin Ren establish a connection between nondeterministic algorithms estimating the acceptance probability of a given circuit and average-case lower bounds for nondeterministic time classes. ``Improved Bounds for Perfect Sampling of $k$-Colorings in Graphs" by Siddharth Bhandari and Sayantan Chakraborty presents a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $\Delta$ and an integer $k>3\Delta$ and returns a random proper $k$-coloring of $G$. We thank the authors, the STOC 2020 program committee, the STOC 2020 external reviewers, and the SICOMP referees for all of their hard work. Arkadev Chattopadhyay, Marek Cygan, Noga Ron-Zewi, Christian Wulff-Nilsen - Guest editors

MODELS AND PROCEDURES FOR CLASSIFICATION AND FORECASTING OF PROCESS PARAMETERS ACCORDING TO CHAOTIC DYNAMICS

The report investigates the processes of modeling and short-term prediction of nondeterministic time sequences, which are anti-persistent time series (AРТS) according to the classification based on the Hearst parameter. The subject of analysis is the numerical procedures for classification and forecasting the parameters of such models. The aim of the work was to increase the efficiency and accuracy of methods and algorithms for classification, modeling and forecasting of AРТS. The objectives of the study were to develop by aggregating the levels of AРТS mathematical models for the classification of time series, as well as the formation of algorithmic and software tools. The report also presents a tool software environment that provides a correct study of modeling algorithms and classification of AРТS.

Models and procedures for classification and forecasting of nondeterministic processes according to chaotic dynamics parameters

The article investigates the processes of classification, modeling and short-term prediction of nondeterministic time sequences, which are represented by antipersistent time series (ATS). The subject of analysis - procedures for classification and forecasting the pa-rameters of such models. The object of research is the processes of modeling and analysis of parameters of nondeterministic time series of ATS with a uniform step. The aim of the work is to increase the efficiency and accuracy of methods and algorithms for classification, modeling and forecasting of ATS. Models and methods of fractal analysis are used to study the properties of ATS, on the basis of which the categories of processes of numerical series are established. With the help of aggregation of ATS levels correct mathematical models of classification of nondeterministic time sequences are developed, and also algorithmic and software means of their realization are formed. Examples of models of numerical series obtained using the aggregation procedure presented in the study are given. It is established that the most detailed and stable is the classification of ATS based on data aggregation schemes without level crossing. The comparative analysis of numerical efficiency of algorithms of classification of ATS is carried out and the task of formation of procedures of interpolation and short-term forecasting of ATS is realized. An instrumental software environment is presented, which provides a correct study of algorithms for modeling and classification of antipersistent time series. Recommendations on the procedures for modeling ATS classification algorithms are of practical importance.

Toward a generalized notion of discrete time for modeling temporal networks

AbstractMany real-world networks, including social networks and computer networks for example, are temporal networks. This means that the vertices and edges change over time. However, most approaches for modeling and analyzing temporal networks do not explicitly discuss the underlying notion of time. In this paper, we therefore introduce a generalized notion of discrete time for modeling temporal networks. Our approach also allows for considering nondeterministic time and incomplete data, two issues that are often found when analyzing datasets extracted from online social networks, for example. In order to demonstrate the consequences of our generalized notion of time, we also discuss the implications for the computation of (shortest) temporal paths in temporal networks. In addition, we implemented an R-package that provides programming support for all concepts discussed in this paper. The R-package is publicly available for download.

A cerebellar-based solution to the nondeterministic time delay problem in robotic control

The presence of computation and transmission-variable time delays within a robotic control loop is a major cause of instability, hindering safe human-robot interaction (HRI) under these circumstances. Classical control theory has been adapted to counteract the presence of such variable delays; however, the solutions provided to date cannot cope with HRI robotics inherent features. The highly nonlinear dynamics of HRI cobots (robots intended for human interaction in collaborative tasks), together with the growing use of flexible joints and elastic materials providing passive compliance, prevent traditional control solutions from being applied. Conversely, human motor control natively deals with low power actuators, nonlinear dynamics, and variable transmission time delays. The cerebellum, pivotal to human motor control, is able to predict motor commands by correlating current and past sensorimotor signals, and to ultimately compensate for the existing sensorimotor human delay (tens of milliseconds). This work aims at bridging those inherent features of cerebellar motor control and current robotic challenges—namely, compliant control in the presence of variable sensorimotor delays. We implement a cerebellar-like spiking neural network (SNN) controller that is adaptive, compliant, and robust to variable sensorimotor delays by replicating the cerebellar mechanisms that embrace the presence of biological delays and allow motor learning and adaptation.

A framework for hybrid simulation with online model updating suitable for hard real‐time computing

The hybrid simulation method is used to test one or some components of a prototype structure subjected to a plausible loading history, accounting for their interaction with the untested ones, which are simulated numerically. If tested components have similar numerical counterparts, a possible approach to reduce simulation errors is to update the parameters of numerical substructures based on tested physical substructures. For this reason, online parameter estimation has gained the attention of the hybrid simulation community in the last decade. The term online indicates that the parameters of the identification model of the physical substructure are updated during the experiment. Main state-of-the-art middleware tools (e.g., OpenFresco and UI-SIMCOR) have been extended to support online model updating for the pseudodynamic hybrid simulation method. In this case, both numerical substructures and dynamic identification models are implemented on existing finite-element analysis software, which communicates with the middleware using a data exchange protocol with non-deterministic time schedule (e.g., TCP/IP). On the other hand, fast- and real-time hybrid simulation methods require a deterministic data exchange schedule between substructures, which imposes the adoption of hard real-time implementations. In this context, partitioned time integration is proposed to coordinate the parallel execution of simulation and model updating processes with heterogeneous sampling rates. As a result, the allocation of computational resources can leverage parallelization capabilities of multi-core CPUs.

Verifying whether one-tape Turing machines run in linear time

We discuss the following family of problems, parameterized by integers C≥2 and D≥1: Does a given one-tape q-state Turing machine make at most Cn+D steps on all computations on all inputs of length n, for all n? Assuming a fixed tape and input alphabet, we show that these problems are co-NP-complete and we provide good lower bounds. Specifically, these problems cannot be solved in o(q(C−1)/4) nondeterministic time by multi-tape Turing machines. We also show that the complements of these problems can be solved in O(qC+2) nondeterministic time and cannot be solved in o(q(C−1)/4) nondeterministic time by multi-tape Turing machines.

A Modular Real-time Tidal Prediction Model based on Grey-GMDH Neural Network

ABSTRACTReal-time prediction of tidal level is of great significance for activities of human beings in the fields of marine and coastal engineering. However, the disturbance factors of tidal level are very intricate, which deteriorate the tidal prediction accuracy. To improve the accuracy of real-time tidal-level prediction, a modular real-time tidal-level prediction approach is proposed based on the grey group method of data handling (Grey-GMDH) neural network. The modular model is composed of astronomical tide parts caused by celestial bodies’ movement and the nonastronomical tide parts caused by various meteorological and other environmental factors. The GMDH is a polynomial network that is commonly used in prediction and pattern recognition. However, GMDH is sensitive to nondeterministic time series, which would result in low accuracy of prediction. In this study, the grey prediction theory is introduced into the GMDH prediction model to alleviate the unfavorable effects of uncertainty caused by various environmental factors and the adverse effects caused thereby on the prediction accuracy. In this study of tidal prediction, the Grey-GMDH model is used to predict the nonastronomical tide parts, whereas the conventional harmonic analysis model is used to predict the astronomical tide parts. The final prediction result is achieved by combining the estimation outputs of the harmonious analysis model and the Grey-GMDH model. Measured tidal-level data of San Diego tidal station is selected as the testing database. Simulation and experimental results confirm that the proposed approach can achieve real-time predictions for tidal level with high accuracy, satisfactory convergence and stability.

Local reduction

We reduce non-deterministic time T≥2n to a 3SAT instance ϕ of quasilinear size |ϕ|=T⋅logO(1)⁡T such that there is an explicit NC0 circuit C that encodes ϕ in the following way: on input a (log⁡|ϕ|)-bit index i, C outputs the ith clause of ϕ. The previous best result was C in NC1. Even in the simpler setting of polynomial size (|ϕ|=poly(T)), the previous best result was C in AC0.More generally, for any time T≥n and parameter r≤n we obtain |ϕ|=max⁡(T,2n/r)⋅(nlog⁡T)O(1), and each output bit of C is a decision tree of depth O(log⁡r).As an application, we tighten Williams' connection between satisfiability algorithms and circuit lower bounds (STOC 2010; SIAM J. Comput. 2013).

Justification of Wold’s Theorem and the Unbiasedness of a Stable Vector Autoregressive Time Series Model Forecasts

In this work, the multivariate analogue to the univariate Wold’s theorem for a purely non-deterministic stable vector time series process was presented and justified using the method of undetermined coefficients. By this method, a finite vector autoregressive process of order [] was represented as an infinite vector moving average () process which was found to be the same as the Wold’s representation. Thus, obtaining the properties of a process is equivalent to obtaining the properties of an infinite process. The proof of the unbiasedness of forecasts followed immediately based on the fact that a stable VAR process can be represented as an infinite VEMA process.

Performance Evaluation for Interrupt-Driven Embedded Software Based on EDSPN

In the design of trustworthy software for real-time embedded systems, the interrupt mechanism plays an important role. Due to the randomness and non-determinism of interrupt handling behaviors, the performance evaluation of embedded software is an important but challenging problem. To solve this problem, we propose a performance model for embedded software based on extended deterministic and stochastic Petri nets (EDSPN), which is a semantic expansion of DSPN that add non-deterministic time transitions. In this manner, the performance model can effectively express interrupt handling behaviors, including random requests, responses according to priority, interrupt nesting, and non-deterministic execution times. In addition, we also provide a performance evaluation method for the EDSPN model based on Markov regenerative theory and demonstrate the analysis process via a specific example. Finally, we analyze the performance of embedded software, taking into account all types of the impact factors of interrupts through experimentation.

A Feedback-oriented Data Delay Modeling in a Dynamic Neural Network for Time Series Forecasting

In this study, we develop a neural network with a time shifting approach to forecast time series patterns. We investigate the impact of different layer-weight configurations to capture the trends in the forms of seasonal, chaotic, etc. We also hypothesize the combined effect of the delayed inputs and the forward connections to introduce a dynamical structure. The effect of overfitting issue is procedurally monitored to gain the resistance property from the early stoppage of training process and to reduce the predictions' error. Finally, the performance of the proposed network is challenged by six well-known deterministic and non-deterministic time series and compared by the autoregression (AR), artificial neural network (ANN), adaptive k-nearest neighbors (AKN), and adaptive neural network (ADNN) models. The results show that the proposed network outperforms the conventional models, particularly in forecasting the chaotic and seasonal time series.

Analytical properties of resource-bounded real functionals

Computable analysis is an extension of classical discrete computability by enhancing the normal Turing machine model. It investigates mathematical analysis from the computability perspective. Though it is well developed on the computability level, it is still under developed on the complexity perspective, that is, when bounding the available computational resources. Recently Kawamura and Cook developed a framework to define the computational complexity of operators arising in analysis. Our goal is to understand the effects of complexity restrictions on the analytical properties of the operator. We focus on the case of norms over C[0, 1] and introduce the notion of dependence of a norm on a point and relate it to the query complexity of the norm. We show that the dependence of almost every point is of the order of the query complexity of the norm. A norm with small complexity depends on a few points but, as compensation, highly depends on them. We briefly show how to obtain similar results for non-deterministic time complexity. We characterize the functionals that are computable using one oracle call only and discuss the uniformity of that characterization.

RPATS – Reliable power aware time synchronization protocol

Many applications of Wireless Sensor Networks (WSNs) need the local clocks of the individual sensor nodes (SN) to be synchronized. Almost any form of sensor data fusion or coordinated actuation requires synchronized physical time for reasoning about events in the physical world. However, while the clock accuracy and precision requirements are often stricter in WSN than in traditional distributed systems, energy and channel constraints limit the resources available to meet these goals. In this paper, we present a power aware time synchronization protocol, of type sender–receiver, suitable for implementation in duty-cycled WSN. By using this proposal most of the non-deterministic time delays during packet transfer (media access, waiting packets in queues, propagation delay) as dominant ones (order of several hundred milliseconds), in respect to data processing (interrupt handling, testing status registers in program loop) as minor (up to hundred microseconds), are bypassed. In addition reliable and unreliable data transfer between SNs is considered. With aim to compensate SN’s oscillator instability, i.e. error in time synchronization, we propose duty cycle time extension. Apart from that, in order to evaluate the low-power capability of the proposed protocol we have involved quantitative performance metric called lifetime efficiency and compared it with equivalent (same) metric of the well known Reference-Broadcast Synchronization, RBS, and Timing-sync Protocol for Sensor Networks, TPSN, protocols, for different error prone environment and different period of time synchronization.

ON CENTRALIZED PARALLEL COMMUNICATING GRAMMAR SYSTEMS WITH CONTEXT-SENSITIVE COMPONENTS

Centralized parallel communicating grammar systems with context-sensitive components that work in returning mode can only generate context-sensitive languages. Here we show that, when working in nonreturning mode, these grammar systems generate all languages from the nondeterministic time complexity class NEXT = ∪c ≥ 1 NTIME (2c·n).

Testing Super-Deterministic Hidden Variables Theories

We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect a super-deterministic modification of quantum mechanics to become relevant.