Nisrean Thalji · 2024
Swarm-based optimization algorithms (SBOAs) have demonstrated effectiveness in solving complex problems within a reasonable time. Among these algorithms, the intelligent water drops algorithm (IWD) has recently gained attention for its ability to provide acceptable solutions to difficult problems. The aim of this research is to evaluate the efficiency of the IWD algorithm in addressing the graph coloring problem (GCP), which is a problem that is notoriously difficult to solve and falls under the category of nondeterministic polynomial (NP) hard problems. The algorithm uses multiple drops and cycles to improve solution quality. Experiments show the presented algorithm outperforms the genetic algorithm with multipoint guided mutation for graph coloring (GAMGMGC) and ant-based algorithm for coloring graphs (ABAC) in terms of execution time. Findings advocate additional research on the use of SBOAs, particularly the IWD algorithm, for solving other (NP) hard problems
Cited by 0
Hiroshi Sakai, Mao Wu, Michinori Nakata · International Journal of Intelligent Systems · 2013
We have been proposing a framework rough Nondeterministic information analysis, which considers granular computing concepts in tables with incomplete and nondeterministic information, as well as rule generation. We have recently defined an expression named division chart with respect to an implication and a subset of objects. Each division chart takes the role of the minimum granule for rule generation, and it takes the role of contingency table in statistics. In this paper, we at first define a division chart in deterministic information systems (DISs) and clarify the relation between a division chart and a corresponding implication. We also consider a merging algorithm for two division charts and extend the relation in DISs to nondeterministic information systems. The relation gives us the foundations of rule generation in tables with nondeterministic information.
Cited by 7
Dimitris J. Kavvadias, Elias C. Stavropoulos · 2001
In 1996, Fredman and Khachiyan [Journal of Algorithms, 21:618--628, 1996] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone disjunctive normal forms. Their algorithm runs in n time, thus giving evidence that the problem lies in an intermediate class between P and co-NP. In this paper we show that a modified version of their algorithm requires deterministic n) nondeterministic guesses, thus placing the problem in the class co-NP[log n]. Our version of the algorithm has also the advantage of having a simpler analysis than its deterministic one.
Cited by 0
Scott Diehl, Ryan Williams, Dieter Van Melkebeek · Minds at UW (University of Wisconsin) · 2007
We show that for all reals c and d such that c 2 d < 4 there exists a positive real e such that tautologies cannot be decided by both a nondeterministic algorithm that runs in time n c, and a nondeterministic algorithm that runs in time n d and space n e. In particular, for every real d < 3 √ 4 there exists a positive real e such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e. 1
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Igor Walukiewicz, et al. · 2004
We show an algorithm which, for a given deterministic parity automaton on infinite trees, computes the minimal Mostowski (or Rabin) index of a nondeterministic automaton recognizing the same language. This extends a previous result of Urba'nski on deciding if a given deterministic Rabin automaton is equivalent to a nondeterministic B"uchi automaton. The algorithm runs in the time of verifying the non-emptiness of nondeterministic parity automata.
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Scott Diehl, Dieter van Melkebeek, Ryan Williams · 2010
We show that for all reals c and d such that c 2 d < 4 there exists a positive real e such that tautologies of length n cannot be decided by both a nondeterministic algorithm that runs in time n c, and a nondeterministic algorithm that runs in time n d and space n e. In particular, for every d < 3√ 4 there exists a positive e such that tautologies cannot be decided by a nondeterministic algorithm that runs in time n d and space n e.
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Jianming Zhou · arXiv (Cornell University) · 2013
This paper demonstrates the relativity of Computability and Nondeterministic; the nondeterministic is just Turing's undecidable Decision rather than the Nondeterministic Polynomial time. Based on analysis about TM, UM, DTM, NTM, Turing Reducible, beta-reduction, P-reducible, isomorph, tautology, semi-decidable, checking relation, the oracle and NP-completeness, etc., it reinterprets The Church-Turing Thesis that is equivalent of the Polynomial time and actual time; it redefines the NTM based on its undecidable set of its internal state. It comes to the conclusions: The P-reducible is misdirected from the Turing Reducible with its oracle; The NP-completeness is a reversal to The Church-Turing Thesis; The Cook-Levin theorem is an equipollent of two uncertains. This paper brings forth new concepts: NP (nondeterministic problem) and NP-algorithm (defined as the optimal algorithm to get the best fit approximation value of NP). P versus NP is the relativity of Computability and Nondeterministic, P/=NP. The NP-algorithm is effective approximate way to NP by TM.
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Khaled El‐Fakih, Roland Groz, Muhammad Naeem Irfan et al. · HAL (Le Centre pour la Communication Scientifique Directe) · 2010
Learning models from test observations can be adapted to the case when the system provides nondeterministic answers. In this paper we propose an algorithm for inferring observable nondeterministic finite state machines (ONFSMs). The algorithm is based on Angluin L* algorithm for learning DFAs. We define rules for constructing and updating learning queries taking into account the properties of ONFSMs. Application examples, complexity analysis and an experimental evaluation of the proposed algorithm are provided.
Cited by 15Open access
Melnikov Boris Feliksovich · CyberLeninK (CyberLeninka)
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Hikmat Farhat · IEEE Transactions on Automatic Control · 2020
In this article, we investigate the synthesis of a (possibly nondeterministic) supervisor, with partial information, such that the controlled nondeterministic plant is bisimulation equivalent to a nondeterministic specification. We derive a new necessary and sufficient condition for the existence of a supervisor and provide an algorithm for the supervisor construction when one exists. The algorithm is exponential in the size of the plant and specification, a substantial improvement over the double exponential cost from exhaustive search. We show that the cases of complete information and deterministic control are special cases of the presented theory.
Cited by 9
Alina Dubrovska · arXiv (Cornell University) · 2006
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function.
Cited by 3Open access
Vivek Anand T Kallampally, Raghunath Tewari · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2016
Savitch showed in 1970 that nondeterministic logspace (NL) is contained in deterministic O(log^2(n)) space but his algorithm requires quasipolynomial time. The question whether we can have a deterministic algorithm for every problem in NL that requires polylogarithmic space and simultaneously runs in polynomial time was left open. In this paper we give a partial solution to this problem and show that for every language in NL there exists an unambiguous nondeterministic algorithm that requires O(log^2(n)) space and simultaneously runs in polynomial time.
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Vasilieva, Alina Dubrovska · arXiv (Cornell University) · 2006
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function.
Cited by 0Open access
S.-J. Park, J.-T. Lim · 2002
Considers the nonblocking supervisory control problems of nondeterministic discrete event systems (DESs) which are modeled as nondeterministic automata with /spl epsiv/-moves. Based on language models, the paper presents the necessary and sufficient conditions for the existence of a nonblocking supervisor to achieve a given language specification for a nondeterministic DES. The developed nonblocking supervisor always guarantees the absence of blocked states in a controlled nondeterministic system. Moreover, when the language specification does not satisfy the existence conditions, the paper provides the computational algorithm for finding the supremal language of the specification which satisfies the conditions. Furthermore, the results developed are demonstrated through the example of an assembly work station.
Cited by 1
Christian Bianchini, Alberto Policriti, Brian Riccardi et al. · Theoretical Computer Science · 2024
We tackle the (classic) problem of minimizing (non)deterministic finite automata. The algorithm we put forward has the peculiarity of being incremental, i.e., the minimization proceeds by successive iterations, each producing a partially minimized automaton language-equivalent to the input one. Our algorithm builds upon Almeida et al. from 2014, fixing a minor mistake and generalizing it to the nondeterministic case. It relies on a coloring procedure of a graph associated to the automaton, keeping track of partial information. After dealing with the deterministic case, we extend this idea to the bisimulation-minimization of nondeterministic automata. The algorithms for both the deterministic and the nondeterministic cases run in time O(nm) for an automaton with n states and m transitions. The complexity for the deterministic case matches the complexity claimed by Almeida et al.. The nondeterministic case improves the fastest known incremental algorithm for this problem. We conclude introducing and using a notion of signature of a state, whose aim is to exploit pre-computed information potentially available, to speed-up the process. A signature is used to produce an initial partition of the automaton's states and can be easily integrated in both the incremental and the non-incremental algorithm.
Cited by 5Open access
Hui Deng · Research Square · 2023
Abstract Efficient and effective modeling of complex real-world situations characterized by uncertainty poses a substantial challenge. This study addresses this challenge by introducing a nondeterministic fuzzy abstraction approach to enhance efficiency and effectiveness in this context. The theoretical framework establishes a standardized representation of nondeterministic fuzzy Kripke structures, accompanied by definitions associated with nondeterministic fuzzy abstraction. The methods section presents an algorithm for realizing nondeterministic fuzzy abstraction, and it is well-suited for practical implementation in computer programs. The results section demonstrates the practical application of the proposed approach by modeling the process of treating a patient with ulcers in the terminal ileum. In the discussion section, a comparative study of nondeterministic fuzzy abstraction underscores its broad applicability and compatibility across various uncertainty and certainty model structures.
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Jorge A. Ruíz-Vanoye, Ocotlán Díaz-Parra, Francisco R. Trejo-Macotela et al. · International Journal of Combinatorial Optimization Problems and Informatics. · 2020
P versus NP is an unsolved problem in mathematics and computational complexity. In this paper, we use the formal language theory to the computational complexity to analyze P versus NP problem from a new point of view. P versus NP problem is to determine whether some deterministic algorithm also accepts every language accepted by some nondeterministic algorithm in polynomial time in polynomial time. Then, we use the theory of formal languages to determine whether some deterministic algorithm also accepts every language accepted by some nondeterministic algorithm in polynomial time in polynomial time. We use different problems to display the question of P versus NP from Formal Languages Theory View.
Cited by 1Open access
Renato Markele Ferreira Cândido, Laurent Hardouin, Mehdi Lhommeau et al. · IEEE Transactions on Automatic Control · 2020
Max-plus linear (MPL) systems are often described by a transition function, which models the state evolution of the system, and a measurement function, which binds the measures with the system states. Methods for computing the inverse image of a point w.r.t. the measurement function are particularly interesting in applications where it is desirable to obtain information about the system states based on the output observations. The inverse image of a set w.r.t. a nondeterministic MPL system, called uncertain MPL (uMPL) system, can be computed by using the difference-bound matrices (DBM) approach. In this article, we aim to use an interval analysis to propose a method to compute the inverse image of a point w.r.t. an uMPL system. The algorithm proposed has a lower worst-case complexity compared with the DBM approach as previously proposed in the literature.
Cited by 8Open access
Eleftherios I. Amoiralis, Marina A. Tsili, Dimitrios G. Paparigas et al. · IEEE Transactions on Industry Applications · 2014
This paper compares the application of two deterministic and three nondeterministic optimization algorithms to global transformer design optimization (TDO). Two deterministic optimization algorithms (mixed-integer nonlinear programming and heuristic algorithm) are compared to three nondeterministic approaches (harmony search, differential evolution, and genetic algorithm). All these algorithms are integrated in design optimization software applied and verified in the manufacturing industry. The comparison yields significant conclusions on the efficiency of the algorithms and the selection of the most suitable one for the TDO problem.
Cited by 48
Alvin Syarifudin Shahab, Dadet Pramadihanto, Sritrusta Sukaridhoto et al. · 2017
Memory management evaluation test is one of the ways to understand the characteristic and performance of dynamic memory allocation algorithm. DMA is one of the RTOS parts that provide storage management when the applications are running. Nowadays there is a lot of memory management algorithm, and each algorithm has its own characteristics like the deterministic or nondeterministic algorithm. We develop a testing framework using Markov chain in order to test the allocation algorithm performance to fit the allocation behavior in RTOS. The framework generates various type of scenario test which can determine deterministic and nondeterministic of the algorithm based on the performance result. The result shows the impact of allocation size and allocation variation affect the allocation performance respond that generated by this framework.
Cited by 1