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About 1,084 papers for “Nondeterministic algorithm”

A Nondeterministic Minimization Algorithm

Bruno Caprile, Federico Girosi · 1990

The problem of minimizing a multivariate function is recurrent in many disciplines as Physics, Mathematics, Engeneering and, of course, Computer Science. In this paper we describe a simple nondeterministic algorithm which is based on the idea of adaptive noise, and that proved to be particularly effective in the minimization of a class of multivariate, {\it continuous valued, smooth functions}, associated with some recent extension of regularization theory by Poggio and Girosi (1990). Results obtained by using this method and a more traditional gradient descent technique are also compared.

Cited by 20

Is Your Graph Algorithm Eligible for Nondeterministic Execution?

Zhiyuan Shao, Lin Hou, Yan Ai et al. · 2015

Graph algorithms are used to implement data mining tasks on graph data-sets. Besides conducting the algorithms by the default deterministic manner, some graph processing frameworks, especially those supporting asynchronous execution model, provide interfaces for the algorithms to be executed in nondeterministic manner, which can improve the scalability and performance of the algorithm's executions. However, is the graph algorithm eligible for nondeterministic execution, and will the execution produce expected results? The literature gives few answers to these questions. In this paper, we study the nondeterministic execution of graph algorithms by considering the scenario where data dependences happen in the edges in graph processing frameworks that employ asynchronous execution model. Our study reveals that only by guaranteeing the atomicity of individual reads and writes, some algorithms (e.g., Graph traversal algorithms) can converge by recovering from corrupted intermediate results with nondeterministic execution, and thus tolerate even write-write conflicts, while some other algorithms (e.g., Fixed point iteration algorithms) can converge but tolerate only read-write conflicts. By conducting graph algorithms on real-world graphs in Graph Chi, and comparing their performances and results with deterministic executions, we find that their performance gains are generally scalable to the available processors with nondeterministic executions, and the results at convergence of fixed point iteration algorithms from nondeterministic executions exhibit larger variances from one run to another than their deterministic executions.

Cited by 3

Generating Minimal Nondeterministic Finite Automata Using a Parallel Algorithm

Tomasz Jastrząb, Zbigniew J. Czech, Wojciech Wieczorek · 2020

The goal of this paper is to develop a parallel algorithm that, on input of a learning sample, identifies a regular language by means of a nondeterministic finite automaton (NFA). A sample is a pair of finite sets containing positive and negative examples. Given a sample, a minimal NFA or the range of possible sizes of such an NFA, that represents the target regular language is sought. We define the task of finding an NFA, which accepts all positive examples and rejects all negative ones, as a constraint satisfaction problem, and then propose a parallel algorithm to solve the problem. The results of computational experiments on the variety of test samples are reported.

Cited by 1

Fast Nondeterministic Matrix Multiplication via Derandomization of Freivalds' Algorithm.

Jiřı́ Wiedermann · 2014

We design two nondeterministic algorithms for matrix multiplication. Both algorithms are based on derandomization of Freivalds’ algorithm for verification of matrix products. The first algorithm works with real numbers and its time complexity on Real RAMs is O(n 2logn). The second one is of the same complexity, works with integer matrices on a unit cost RAM with numbers whose size is proportional to the size of the largest entry in the underlying matrices. Our algorithms bring new ideas into the design of matrix multiplication algorithms and open new avenues for their further development. The results pose exciting questions concerning the relation of the complexity of deterministic versus nondeterministic algorithms for matrix multiplication, and complexity of integer versus real matrices multiplication.

Cited by 0

An Algorithm for Matching Nondeterministic Services with Operating Guidelines

Peter Massuthe, Karsten Wolf · edoc Publication server (Humboldt University of Berlin) · 2006

Interorganizational cooperation is more and more organized by the paradigm of services. Service-oriented architectures (SOA) provide a general framework for service interaction. SOA describe three roles of services, the service provider, the service requester, and the service broker, together with the three operations publish, find, and bind. We provide a formal method based on nondeterministic automata to model services and their interaction. In this paper, we restrict ourselves to finite and acyclic automata. We suggest operating guidelines as a convenient and intuitive artifact to realize the publish operation. In our approach, the find operation reduces to a matching problem between the requester’s service and the published operating guidelines. If matching services are actually bound together, our approach guarantees deadlockfree communication. In this paper, matching of deterministic as well as nondeterministic automata with operating guidelines is presented.

Cited by 13Open access

A Practical Algorithm for Reducing Nondeterministic Finite State Automata

Michael Albert, S. Linton, Michael Albert A et al. · 2004

In [3], Ilie and Yu describe a construction of a right-invariant equivalence relation on the states of a non-deterministic finite-state automaton. We give a more e#- cient algorithm for constructing the same equivalence, together with results from a computer implementation.

Cited by 4

An algorithm to find optimal attack paths in nondeterministic scenarios

Carlos Sarraute, Gerardo Richarte, Jorge Lucángeli Obes · arXiv (Cornell University) · 2011

As penetration testing frameworks have evolved and have become more complex, the problem of controlling automatically the pentesting tool has become an important question. This can be naturally addressed as an attack planning problem. Previous approaches to this problem were based on modeling the actions and assets in the PDDL language, and using off-the-shelf AI tools to generate attack plans. These approaches however are limited. In particular, the planning is classical (the actions are deterministic) and thus not able to handle the uncertainty involved in this form of attack planning. We herein contribute a planning model that does capture the uncertainty about the results of the actions, which is modeled as a probability of success of each action. We present efficient planning algorithms, specifically designed for this problem, that achieve industrial-scale runtime performance (able to solve scenarios with several hundred hosts and exploits). These algorithms take into account the probability of success of the actions and their expected cost (for example in terms of execution time, or network traffic generated). We thus show that probabilistic attack planning can be solved efficiently for the scenarios that arise when assessing the security of large networks. Two "primitives" are presented, which are used as building blocks in a framework separating the overall problem into two levels of abstraction. We also present the experimental results obtained with our implementation, and conclude with some ideas for further work.

Cited by 30Open access

A Genetic Algorithm for the Induction of Nondeterministic Pushdown Automata

Marc M. Lankhorst, Marc M. Lankhorst · 1995

This paper presents a genetic algorithm used to infer pushdown automata from legal and illegal examples of a language. It gives an introduction into grammatical inference, and discusses related work in grammatical inference using genetic algorithms. The paper describes the type of automaton that is used, the evaluation of the fitness of automata with respect to a set of examples of a language, the representation of automata in the genetic algorithm, and the genetic operators that work on this representation. Results are reported on the inference of a test suite of 10 languages. Pushdown automata for the language of correctly balanced and nested parentheses expressions, the language of sentences containing an equal number of a's and b's, the two-symbol palindromes, a set of regular languages, and a small natural language subset were inferred. Furthermore, some possible improvements and extensions of the algorithm are discussed. 1 Introduction Genetic algorithms, introduced by Holland (...

Cited by 0

A Nondeterministic Parallel Algorithm for General Unsymmetric Sparse LU Factorization

Timothy A. Davis, Pen-Chung Yew · SIAM Journal on Matrix Analysis and Applications · 1990

A parallel algorithm for the direct LU factorization of general unsymmetric sparse matrices is presented. The algorithm D2 is based on a new nondeterministic parallel pivot search that finds a compatible pivot set${\bf S}$ of size m, followed by a parallel rank-m update. These two steps alternate until switching to dense matrix code or until the matrix is factored. The algorithm is based on a shared-memory multiple-instruction-multiple-data (MIMD) model and takes advantage of both concurrency and (gather-scatter) vectorization. The detection of parallelism due to sparsity is based on Markowitz’s strategy, an unsymmetric ordering method. As a result, D2 finds more potential parallelism for matrices with highly asymmetric nonzero patterns than algorithms that construct an elimination tree using a symmetric ordering method (minimum degree or nested dissection, for example) applied to the symmetric pattern of ${\bf A} + {\bf A}^{\bf T} $ or ${\bf A}^{\bf T} {\bf A}$. The pivot search exploits more parallelism than previous algorithms that are based on unsymmetric ordering methods. Possible extensions to the D2 algorithm are discussed, including the use of dense matrix kernels and a software-combining tree to enhance parallelism in the pivot search.

Cited by 50

On Nondeterministic Derandomization of Freivalds' Algorithm: Consequences, Avenues and Algorithmic Progress

Marvin Künnemann · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2018

Motivated by studying the power of randomness, certifying algorithms and barriers for fine-grained reductions, we investigate the question whether the multiplication of two n x n matrices can be performed in near-optimal nondeterministic time O~(n^2). Since a classic algorithm due to Freivalds verifies correctness of matrix products probabilistically in time O(n^2), our question is a relaxation of the open problem of derandomizing Freivalds' algorithm. We discuss consequences of a positive or negative resolution of this problem and provide potential avenues towards resolving it. Particularly, we show that sufficiently fast deterministic verifiers for 3SUM or univariate polynomial identity testing yield faster deterministic verifiers for matrix multiplication. Furthermore, we present the partial algorithmic progress that distinguishing whether an integer matrix product is correct or contains between 1 and n erroneous entries can be performed in time O~(n^2) - interestingly, the difficult case of deterministic matrix product verification is not a problem of "finding a needle in the haystack", but rather cancellation effects in the presence of many errors. Our main technical contribution is a deterministic algorithm that corrects an integer matrix product containing at most t errors in time O~(sqrt{t} n^2 + t^2). To obtain this result, we show how to compute an integer matrix product with at most t nonzeroes in the same running time. This improves upon known deterministic output-sensitive integer matrix multiplication algorithms for t = Omega(n^{2/3}) nonzeroes, which is of independent interest.

Cited by 6Open access

An algorithm for computing supremal nonblocking state-normal supervisors for nondeterministic systems

Rong Su, Jan H. van Schuppen, Jacobus E. Rooda · 2009

Recently supervisor synthesis for nondeterministic systems has gained more and more attention, owing to the potential computational advantage of using nondeterministic automata in modular/distributed synthesis. It is well known that, in the Ramadge/Wonham language-based supervisory control paradigm, the supremal nonblocking normal supervisor always exists (although may be empty) and is computable. In this paper we will show that, for a nondeterministic plant model and a deterministic specification, a similar entity called the supremal nonblocking state-normal supervisor also exists, which coincides with the supremal nonblocking normal supervisor when the plant model becomes deterministic. We then present a concrete algorithm to compute such a supervisor and analyze the relevant computational complexity.

Cited by 0