Georgel Calin, Pepijn Crouzen, Pedro R. D’argenio et al. · 2010
Abstract. We develop an algorithm to compute timed reachability pro-babilities for distributed models which are both probabilistic and nondeterministic. To obtain realistic results we consider the recently in-troduced class of (strongly) distributed schedulers, for which no analysis techniques are known. Our algorithm is based on reformulating the nondeterministic models as parametric ones, by interpreting scheduler decisions as parameters. We then apply the PARAM tool to extract the reachability probability as a polynomial function, which we optimize using nonlinear programming.
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Jiulei Jiang, Panqing Zhang, Zhanyou Ma · Applied Sciences · 2020
Model checking is a formal automatic verification technology for complex concurrent systems. It is used widely in the verification and analysis of computer software and hardware systems, communication protocols, security protocols, etc. The generalized possibilistic μ-calculus model-checking algorithm for decision processes is studied to solve the formal verification problem of concurrent systems with nondeterministic information and incomplete information on the basis of possibility theory. Firstly, the generalized possibilistic decision process is introduced as the system model. Then, the classical proposition μ-calculus is improved and extended, and the concept of generalized possibilistic μ-calculus (GPoμ) is given to describe the attribute characteristics of nondeterministic systems. Then, the GPoμ model-checking algorithm is proposed, and the model-checking problem is simplified to fuzzy matrix operations. Finally, a specific example and a case study are analyzed and verified. Compared with the classical μ-calculus, the generalized possibilistic μ-calculus has a stronger expressive power and can better characterize the attributes of nondeterministic systems. The model-checking algorithm can give the possibility that the system satisfies the attributes. The research work provides a new idea and method for model checking nondeterministic systems.
Cited by 2Open access
Peifeng Wang · Bulletin of Miscellaneous Information (Royal Gardens Kew)
The execution of an algorithm on computing machines is studied. By Cantor's diagonal argument, we show that, the number of executions within a computation on a nondeterministic Turing machine is asymptotically greater than the number of steps within a computation on a deterministic Turing machine. Thus a nondeterministic machine can have more computing power than a deterministic machine, therefore suggesting P != NP.
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Coz Velasco, Juan José del, Díez Peláez, Jorge, Bahamonde Rionda, Antonio · Consultation of the Doctoral Thesis Database (TESEO) (Ministerio de Educación, Cultura y Deporte) · 2013
Nondeterministic classifiers are defined as those allowed to predict more than one class for some entries from an input space. Given that the true class should be included in predictions and the number of classes predicted should be as small as possible, these kind of classifiers can be considered as Information Retrieval (IR) procedures. In this paper, we propose a family of IR loss functions to measure the performance of nondeterministic learners. After discussing such measures, we derive an algorithm for learning optimal nondeterministic hypotheses. Given an entry from the input space, the algorithm requires the posterior probabilities to compute the subset of classes with the lowest expected loss. From a general point of view, nondeterministic classifiers provide an improvement in the proportion of predictions that include the true class compared to their deterministic counterparts; the price to be paid for this increase is usually a tiny proportion of predictions with more than one class. The paper includes an extensive experimental study using three deterministic learners to estimate posterior probabilities: a multiclass Support Vector Machine (SVM), a Logistic Regression, and a Na¨ıve Bayes. The data sets considered comprise both UCI multi-class learning tasks and microarray expressions of different kinds of cancer. We successfully compare nondeterministic classifiers with other alternative approaches. Additionally, we shall see how the quality of posterior probabilities (measured by the Brier score) determines the goodness of nondeterministic predictions
Cited by 0Open access
Del Coz, Jorge Díez, Antonio Bahamonde et al. · 2014
Nondeterministic classifiers are defined as those allowed to predict more than one class for some entries from an input space. Given that the true class should be included in predictions and the number of classes predicted should be as small as possible, these kind of classifiers can be considered as Information Retrieval (IR) procedures. In this paper, we propose a family of IR loss functions to measure the performance of nondeterministic learners. After discussing such measures, we derive an algorithm for learning optimal nondeterministic hypotheses. Given an entry from the input space, the algorithm requires the posterior probabilities to compute the subset of classes with the lowest expected loss. From a general point of view, nondeterministic classifiers provide an improvement in the proportion of predictions that include the true class compared to their deterministic counterparts; the price to be paid for this increase is usually a tiny proportion of predictions with more than one class. The paper includes an extensive experimental study using three deterministic learners to estimate posterior probabilities: a multiclass Support Vector Machine (SVM), a Logistic Regression, and a Naïve Bayes. The data sets considered comprise both UCI multi-class learning tasks and microarray expressions of different kinds of cancer. We successfully compare nondeterministic classifiers with other alternative approaches. Additionally, we shall see how the quality of posterior probabilities (measured by the Brier score) determines the goodness of nondeterministic predictions.
Cited by 0
Radomír Polách, Jan Trávníček, Jan Janoušek et al. · Annals of Computer Science and Information Systems · 2015
Visibly pushdown automata are pushdown automata whose pushdown operations are determined by the input symbol, where the input alphabet is partitioned into three parts for push, pop and local pushdown operations. It is well known that nondeterministic visibly pushdown automata can be determinised. In this paper a new algorithm for the determinisation of nondeterministic visibly pushdown automata is presented. The algorithm improves the existing methods and can result in significantly smaller deterministic pushdown automata. This is achieved in a way that only necessary and accessible states and pushdown symbols are computed and constructed during the determinisation.
Cited by 1Open access
Muhammed Al-Mulhem, T. Al-Maghrabi · IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics) · 1998
This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.
Cited by 32
Veronique Millette, Natalie Baddour · BioMedical Engineering OnLine · 2011
The presented algorithm does allow for the quantification of nondeterministic events but proper care in signal acquisition and processing must be taken to obtain meaningful results.
Cited by 35Open access
Maxim Likhachev, Sven Koenig · 2008
In this paper, we introduce an efficient replanning algorithm for nondeterministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic discretization of continuous domains, resulting in an efficient implementation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains. 1
Cited by 0
Maxim Likhachev, Sven Koenig · 2008
In this paper, we introduce an efficient replanning algorithm for nondeterministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic discretization of continuous domains, resulting in an efficient implementation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains. 1
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В. Г. Найденко · arXiv (Cornell University) · 2001
We show that there cannot be any algorithm that for a given nondeterministic polynomial-time Turing machine determinates whether or not the language recognized by this machine belongs to P
Cited by 0Open access
S.P. Khatri, A. Narayan, S.C. Krishnan et al. · 33rd Design Automation Conference Proceedings, 1996 · 2005
We propose a new formalism for the Engineering Change (EC) problem in a finite state machine (FSM) setting. Given an implementation that violates the specification, the problem is to alter the behavior of the implementation so that it meets the specification. The implementation can be a pseudo-nondeterministic FSM while the specification may be a nondeterministic FSM. The EC problem is cast as the existence of an "appropriate" simulation relation from the implementation into the specification. We derive the necessary and sufficient conditions for the existence of a solution to the problem. We synthesize all possible solutions, if the EC is feasible. Our algorithm works in space which is linear, and time which is quadratic, in the product of the sizes of implementation and specification. Previous formulations of the problem which admit nondeterministic specifications, although more general, lead to an algorithm which is exponential. We have implemented our procedure using Reduced Ordered Binary Decision Diagrams.
Cited by 10
Bellingham, Matt, Holland, Simon, Mulholland, Paul · Open Research Online (The Open University) · 2016
Algorithmic composition systems allow for the partial or total automation of music composition by formal, computational means. Typical algorithmic composition systems generate nondeterministic music, meaning that multiple musical outcomes can result from the same algorithm - consequently the output is generally different each time the algorithm runs
Cited by 0Open access
М. К. Чирков, A. S. Shevchenko · Vestnik St Petersburg University Mathematics · 2011
Properties of generalized finitely nonstationary nondeterministic automata with an additional random input over a Boolean lattice are considered which are related to the definition of the class of languages represented by such automaton models. New notions of an elementary nondeterministic automatic structure with a random input, of a generalized finitely nonstationary nondeterministic automaton with a random input, of the generalized mapping induced by such an automaton, and of a generalized language represented by such an automaton are introduced. A number of statements substantiating synthesis for any given generalized finitely nonstationary nondeterministic automaton with a random input of an abstract probabilistic finite automaton equivalent to the given one relative to the represented generalized language probabilistic language of the stationary abstract probabilistic finite automaton. The number of states of the synthesized probabilistic automaton is estimated and a synthesis algorithm is developed in detail and illustrated by an example.
Cited by 0
Carlo A. Furia · 2012
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way nondeterministic
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G. Mutyalamma, K. Komali, G. Pushpa · International Journal of Trend in Scientific Research and Development · 2017
In automata theory a minimization is the task of transforming a given finite state machine into an equivalent automation that has a minimum number of states. Here, the reduction of Deterministic Finite Automata(DFA) is very simple whereas Nondeterministic Finite Automata(NFA) is complex because which has maximium number of possible paths to reach new states. So a minimal NFA is a primal problem in automata theory. We consider the problem of approximating a minimal NFA or a minimal regular expression. There are several approaches to NFA minimization either without approximation guarantees or running in at least exponential time. Here this paper introducing the new NFA reduction algorithm for the minimization of NFA. This algorithm will reduce number of state transitions of Nondeterministic Finite Automata. NFA reduction algorithm also resolves the complexity of Kameda-Weiner algorithm. This paper shown empirically that this algorithm is effective in largely reducing the memory requirement of NFA minimization algorithm. Reducing the size of NFA by using NFA Reduction Algorithm has been shown to reduce importantly the search time.
Cited by 0Open access
Alexander Okhotin · 2002
The Generalized LR parsing algorithm for context-free grammars, introduced by Tomita in 1986, is a polynomial-time implementation of nondeterministic LR parsing that uses graph-structured stack to represent the contents of the nondeterministic parser's pushdown for all possible branches of computation at a single computation step. It has been specifically developed as a solution for practical parsing tasks arising in computational linguistics, and indeed has proved itself to be very suitable for natural language processing.
Cited by 0
Naoto Yamaguchi, Mao Wu, Michinori Nakata et al. · Journal of Advanced Computational Intelligence and Intelligent Informatics · 2014
This article reports an application of Rough Nondeterministic Information Analysis (RNIA) to two data sets. One is the Mushroom data set in the UCI machine leaning repository, and the other is a student questionnaire data set. Even though these data sets include many missing values, we obtained some interesting rules by using our getRNIA software tool. This software is powered by the NIS-Apriori algorithm, and we apply rule generation and question-answering functionalities to data sets with nondeterministic values.
Cited by 4Open access
Manfred Schmidt-Schauß, Temur Kutsia, Jordi Levy et al. · Fundamenta Informaticae · 2022
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables representing partial letrec-environments is also shown to be in NP.
Cited by 5Open access
Sankar Gurumurthy, Orna Kupferman, Fabio Somenzi et al. · 2008
Abstract. Several optimal algorithms have been proposed for the complementation of nondeterministic Büchi word automata. Due to the intricacy of the problem and the exponential blow-up that complementation involves, these algorithms have never been used in practice, even though an effective complementation construction would be of significant practical value. Recently, Kupferman and Vardi described a complementation algorithm that goes through weak alternating automata and that seems simpler than previous algorithms. We combine their algorithm with known and new minimization techniques. Our approach is based on optimizations of both the intermediate weak alternating automaton and the final nondeterministic automaton, and involves techniques of rank and height reductions, as well as direct and fair simulation. 1
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