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The descriptive set-theoretic complexity of the set of points of continuity of a multi-valued function

Vassilios Gregoriades, Klaus Weihrauch
2011 Logical Methods in Computer Science  
In this article we treat a notion of continuity for a multi-valued function F and we compute the descriptive set-theoretic complexity of the set of all x for which F is continuous at x.  ...  multi-valued function F whose graph is a Borel set and the set of points of continuity of F is not a Borel set.  ...  assumptions about the complexity of the set F .  ... 
doi:10.2168/lmcs-7(4:2)2011 fatcat:l3ofpilbc5ahheew7m5okouhvi

Complex Neuro-Fuzzy System for Function Approximation

Reza Shoorangiz, Mohammad H. Marhaban
2013 International Journal of Applied Electronics in Physics & Robotics  
Complex fuzzy sets have been developed recently and extends truth values to unit circle in complex plane. Complex fuzzy logic then developed by employing complex fuzzy sets.  ...  In this paper, a novel adaptive complex neuro fuzzy inference system based on complex fuzzy logic is proposed for function approximation.  ...  Complex fuzzy set is the backbone of complex fuzzy logic. The latter is a natural extension of fuzzy logic that benefits from advantages of complex fuzzy sets [5] .  ... 
doi:10.7575/aiac.ijaepr.v.1n.2p.5 fatcat:rcnkd7u3ezhtbdcovrkrm2z5im

Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes

Dan E. Tamir, Abraham Kandel
2011 International Journal of Computers Communications & Control  
The paper surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides an axiomatic basis for first order predicate complex fuzzy logic and complex class  ...  A new interpretation of complex fuzzy membership enables polar and Cartesian representation of the membership function where the two function components carry uncertain information.  ...  Membership-Grade based Definition of Complex Fuzzy Sets A complex fuzzy set S on a universe of discourse U is defined by a complex-valued grade of membership function µ S (x); (Ramot et al.  ... 
doi:10.15837/ijccc.2011.3.2135 fatcat:vyqdx4xsczg23azc6kotcczmee

Hierarchical models of advanced distance protection IEDs

Alexander Apostolov
2014 2014 Power Systems Computation Conference  
Advanced multifunctional distance protection Intelligent Electronic Devices (IEDs) are complex systems with a multi-level functional hierarchy.  ...  Their integration in modern IEC 61850 based substation protection, automation and control systems requires good understanding of their functionality and the IEC 61850 principles of object modeling.  ...  It is clear that the setting data objects in the PDIS defined in Editions 1 and 2 of the IEC 61850 standard are not sufficient to represent the complete complex distance function.  ... 
doi:10.1109/pscc.2014.7038391 dblp:conf/pscc/Apostolov14 fatcat:xzlmooyexvbifih6wxwwl2zznq

Complex Fuzzy Sets and Complex Fuzzy Logic an Overview of Theory and Applications [chapter]

Dan E. Tamir, Naphtali D. Rishe, Abraham Kandel
2015 Studies in Fuzziness and Soft Computing  
In this chapter we reintroduce the concept of complex fuzzy sets and complex fuzzy logic and survey the current state of complex fuzzy logic, complex fuzzy sets theory, and related applications.  ...  Another important extension to the theory, namely the concepts of complex fuzzy logic and complex fuzzy sets, has been investigated by Kandel et al.  ...  Complex Fuzzy Logic and Set Theory The first formalization of complex fuzzy sets and complex fuzzy logic investigated by Kandel and his coauthors [35, 65] is a special case of the formalism presented  ... 
doi:10.1007/978-3-319-19683-1_31 fatcat:xzwgange5rb3vdjimow4se3pvq

Measuring logic complexity can guide pattern discovery in empirical systems

Marco Gherardi, Pietro Rotondo
2016 Complexity  
A definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science was explored.  ...  Detailed numerical analysis shows that (i) logic complexity is effective in discriminating between classes of functions commonly employed in modeling contexts; (ii) it extends the notion of canalization  ...  MEASURING LOGIC COMPLEXITY AND BIAS A Boolean (or logic) function maps the set f0; 1g n to {0, 1}, associating a truth value to each combination of its n Boolean inputs (by convention the integers 1 and  ... 
doi:10.1002/cplx.21819 fatcat:hejkgjnncrbxxecln2ca22l5fy

Page 5150 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
Symbolic Logic 6 (2000), no. 1, 118-119] previously studied the complexity of tabularity, pretabularity, and interpolation problems over the intuitionistic logic (Int) and over modal logic S4.  ...  (RS-AOSSI; Novosibirsk) Complexity of some problems in positive and related calculi. (English summary) Logic and complexity in computer science (Créteil, 2001). Theoret. Comput.  ... 

A comparison of modified reconstructability analysis and Ashenhurst‐Curtis decomposition of Boolean functions

Anas N. Al‐Rabadi, Marek Perkowski, Martin Zwick
2004 Kybernetes  
MRA is compared to Ashenhurst-Curtis (AC) decomposition using two different complexity measures: log-functionality, a measure suitable for machine learning, and the count of the total number of two-input  ...  Modified Reconstructability Analysis (MRA), a novel decomposition technique within the framework of set-theoretic (crisp possibilistic) Reconstructability Analysis, is applied to 3-variable NPN-classified  ...  Example 3 .Figure 6 . 36 For the following logic function F = x 2 x 3 + x 1 x 3 + x 1 x 2 , let the sub-set of variables {x 2 , x 3 } be the Bound Set, and the sub-set of variables {x 1 } be the Free Set  ... 
doi:10.1108/03684920410533985 fatcat:dpgqf3qn6fbynnkzqymt4hy4au

Measuring logic complexity can guide pattern discovery in empirical systems [article]

Marco Gherardi, Pietro Rotondo
2016 arXiv   pre-print
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science.  ...  Detailed numerical analysis shows that (i) logic complexity is effective in discriminating between classes of functions commonly employed in modelling contexts; (ii) it extends the notion of canalisation  ...  Acknowledgements We are thankful to Marco Cosentino Lagomarsino for discussions and useful comments on a previous version of the manuscript.  ... 
arXiv:1603.03337v1 fatcat:xa7f6k6p7rgglmx47a47cytxsu

Expressing versus Proving: Relating Forms of Complexity in Logic

A. Kolokolova
2010 Journal of Logic and Computation  
In particular, we show how the complexity of logics in the setting of finite model theory is used to obtain results in bounded arithmetic, stating which functions are provably total in certain weak systems  ...  Lastly, we will touch upon the topic of formalizing complexity theory using logic, and the meta-question of complexity of logical reasoning about complexity-theoretic statements.  ...  I am very grateful to him for suggesting many of the ideas, as well as the framework in which these connections became natural.  ... 
doi:10.1093/logcom/exq008 fatcat:lpla27ghunf5fmmvdanaoasaei

Multi-Level Implementation of Asynchronous Logic Using Two-Level Nodes

Igor Lemberski, Petr FiŜer
2009 IFAC Proceedings Volumes  
A novel synthesis method of a dual-rail asynchronous multi-level logic is proposed.  ...  Then the implementation complexity of the proposed method and a state-ofthe-art method based on the duplication of every gate was compared. A considerable improvement was obtained.  ...  The complexity of the proposed asynchronous multi-level implementation of the circuits is shown next. Complexities of the functional logic ("Funct.  ... 
doi:10.3182/20091006-3-es-4010.00033 fatcat:qf3ryrsc5faizitiixkmrdqpze

Complexity of Non-Monotonic Logics [article]

Michael Thomas, Heribert Vollmer
2010 arXiv   pre-print
We describe complexity results for fragments of logical languages obtained by either restricting the allowed set of operators (e.g., forbidding negations one might consider only monotone formulae) or by  ...  Complexity results for different reasoning tasks for propositional variants of these logics have been studied already in the nineties.  ...  Seeking further insights into the sources of complexity, abduction has also been studied for restricted sets of Boolean functions.  ... 
arXiv:1009.1990v1 fatcat:wxlr4opy2rez7mgoo2pdcq3fyu

Why complex-valued fuzzy? Why complex values in general? A computational explanation

Olga Kosheleva, Vladik Kreinovich, Thavatchai Ngamsantivong
2013 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS)  
From the mathematical viewpoint, a natural extension of real numbers is the set of complex numbers. Complex-valued fuzzy sets have indeed been successfully used in applications of fuzzy techniques.  ...  In the traditional fuzzy logic, as truth values, we take all real numbers from the interval [0, 1].  ...  1R43TR000173-01 from the National Institutes of Health, and by a grant on F-transforms from the Office of Naval Research.  ... 
doi:10.1109/ifsa-nafips.2013.6608577 dblp:conf/ifsa/KoshelevaKN13 fatcat:e2cqhfcl5rb57ohhp7copqomeu

On the Complexity of Generating Gate Level Information Flow Tracking Logic

Wei Hu, Jason Oberg, Ali Irturk, Mohit Tiwari, Timothy Sherwood, Dejun Mu, Ryan Kastner
2012 IEEE Transactions on Information Forensics and Security  
This paper provides a formal basis for deriving GLIFT logic which includes a proof on the NP-completeness of generating precise GLIFT logic and a formal analysis of the complexity and precision of various  ...  Index Terms-Algorithm design and analysis, Boolean functions, computational complexity, gate level information flow tracking, information security.  ...  ACKNOWLEDGMENT The authors would like to thank the reviewers for their valuable feedback, which was of great help in improving this paper.  ... 
doi:10.1109/tifs.2012.2189105 fatcat:qx4hz5m4vra7dex2zxoippiphm

Page 118 of Automation and Remote Control Vol. 33, Issue 1 [page]

1972 Automation and Remote Control  
To a prime implicant of a logical function there corresponds a maximal complex in the image T(f).  ...  We call the table obtained an m- output logical table: the m-output function is equivalent to a set of m single-output functions fk (k= 1, 2,...,m).  ... 
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