2019, 2nd ed. 2019, ISBN 9783030024192, 511

eBook

Automatica, ISSN 0005-1098, 01/2020, Volume 111, p. 108621

From the new perspective of logical matrix equations, observability of Boolean networks (BNs) is investigated in this paper. First, it is shown that one BN is...

Boolean network | Matrix equation | Observability | Semi-tensor product of matrices | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Boolean network | Matrix equation | Observability | Semi-tensor product of matrices | CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, ISSN 0027-8424, 03/2019, Volume 116, Issue 10, pp. 4123 - 4128

Conventional digital computers can execute advanced operations by a sequence of elementary Boolean functions of 2 or more bits. As a result, complicated tasks...

MEMORY | SYNAPSES | MULTIDISCIPLINARY SCIENCES | analog computing | DEVICES | RRAM | OPTIMIZATION | cross-point architecture | in-memory computing | resistive memory | linear algebra | Usage | Matrices | Research | Mathematical research | Digital integrated circuits | Equations | Digital computers | Computers | Memory devices | Data storage | Boolean algebra | Matrix methods | Analog data | Memory tasks | Boolean functions | Negative feedback | Computation | Mathematical analysis | Differential equations | Schroedinger equation | Eigenvectors | Linear equations | Physical Sciences

MEMORY | SYNAPSES | MULTIDISCIPLINARY SCIENCES | analog computing | DEVICES | RRAM | OPTIMIZATION | cross-point architecture | in-memory computing | resistive memory | linear algebra | Usage | Matrices | Research | Mathematical research | Digital integrated circuits | Equations | Digital computers | Computers | Memory devices | Data storage | Boolean algebra | Matrix methods | Analog data | Memory tasks | Boolean functions | Negative feedback | Computation | Mathematical analysis | Differential equations | Schroedinger equation | Eigenvectors | Linear equations | Physical Sciences

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 02/2018, Volume 64, Issue 2, pp. 1347 - 1360

This paper presents a study of perturbations of symmetric Boolean functions. In particular, it establishes a connection between exponential sums of these...

recurrences | Boolean functions | Blogs | Binomial diophantine equations | exponential sums | perturbations of symmetric Boolean functions | Cryptography | Indexes | Mathematical model | Hamming weight | Perturbations of symmetric Boolean functions | Exponential sums | Recurrences | EXPONENTIAL-SUMS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONJECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Codes | Boolean algebra | Binomial coefficients | Mathematical analysis | Sums | Mathematics - Combinatorics

recurrences | Boolean functions | Blogs | Binomial diophantine equations | exponential sums | perturbations of symmetric Boolean functions | Cryptography | Indexes | Mathematical model | Hamming weight | Perturbations of symmetric Boolean functions | Exponential sums | Recurrences | EXPONENTIAL-SUMS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CONJECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Codes | Boolean algebra | Binomial coefficients | Mathematical analysis | Sums | Mathematics - Combinatorics

Journal Article

Journal of Computer and System Sciences, ISSN 0022-0000, 2010, Volume 76, Issue 3, pp. 251 - 266

Equations with formal languages as unknowns using all Boolean operations and concatenation are studied. Their main properties, such as solution existence and...

Boolean operations | Language equations | Computability | GRAMMARS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, THEORY & METHODS | Mathematical models | Boolean algebra | Recursive | Mathematical analysis | Uniqueness

Boolean operations | Language equations | Computability | GRAMMARS | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, THEORY & METHODS | Mathematical models | Boolean algebra | Recursive | Mathematical analysis | Uniqueness

Journal Article

Publications de l'Institut Mathematique, ISSN 0350-1302, 2015, Volume 98, Issue 112, pp. 85 - 89

Journal Article

Random Structures & Algorithms, ISSN 1042-9832, 03/2018, Volume 52, Issue 2, pp. 197 - 218

We study a random system of cn linear equations over n variables in GF(2), where each equation contains exactly r variables; this is equivalent to r‐XORSAT....

random XORSAT | phase transition | solution geometry | clustering threshold | critical window | BOOLEAN-FORMULAS | MATHEMATICS, APPLIED | ALGORITHM | SAT | GRAPHS | SATISFIABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | VARIABLES | Clusters | Constraint modelling | Statistical analysis | Linear equations | Clustering

random XORSAT | phase transition | solution geometry | clustering threshold | critical window | BOOLEAN-FORMULAS | MATHEMATICS, APPLIED | ALGORITHM | SAT | GRAPHS | SATISFIABILITY | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | VARIABLES | Clusters | Constraint modelling | Statistical analysis | Linear equations | Clustering

Journal Article

1974, ISBN 9780444105202, xix, 442

Book

Random Structures & Algorithms, ISSN 1042-9832, 03/2015, Volume 46, Issue 2, pp. 197 - 231

We consider random systems of linear equations over GF(2) in which every equation binds k variables. We obtain a precise description of the clustering of...

cores | hypergraphs | random k‐XORSAT | solution clustering | Cores | Solution clustering | Hypergraphs | Random k-XORSAT | BOOLEAN-FORMULAS | MATHEMATICS, APPLIED | random k-XORSAT | RESOLUTION | RANDOM HYPERGRAPHS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | CONSTRAINT SATISFACTION PROBLEMS | THRESHOLD | DEGREE SEQUENCE | K-CORE | COMPLEXITY | Sequences | Algorithms | Solution space | Categories | Mathematical analysis | Linear equations | Clustering

cores | hypergraphs | random k‐XORSAT | solution clustering | Cores | Solution clustering | Hypergraphs | Random k-XORSAT | BOOLEAN-FORMULAS | MATHEMATICS, APPLIED | random k-XORSAT | RESOLUTION | RANDOM HYPERGRAPHS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | CONSTRAINT SATISFACTION PROBLEMS | THRESHOLD | DEGREE SEQUENCE | K-CORE | COMPLEXITY | Sequences | Algorithms | Solution space | Categories | Mathematical analysis | Linear equations | Clustering

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2012, Volume 416, pp. 71 - 86

Consider a system of language equations of the form X i = φ i ( X 1 , … , X n ) ( 1 ⩽ i ⩽ n ) , where every φ i may contain the operations of concatenation and...

Language equations | Complementation | Negation | Boolean grammars | Context-free grammars | CONJUNCTIVE GRAMMARS | SETS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Mathematical analysis | Mathematical models | Hierarchies

Language equations | Complementation | Negation | Boolean grammars | Context-free grammars | CONJUNCTIVE GRAMMARS | SETS | COMPUTER SCIENCE, THEORY & METHODS | Computer science | Mathematical analysis | Mathematical models | Hierarchies

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 2007, Volume 181, Issue 3, pp. 1148 - 1165

Microarray chips generate large amounts of data about a cell’s state. In our work we want to analyze these data in order to describe the regulation processes...

Dynamical system | System of piecewise linear differential equations | Gene regulation | Optimization problem | Computational biology | computational biology | optimization problem | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gene regulation | system of piecewise linear differential equations | PROBABILISTIC BOOLEAN NETWORKS | EXPRESSION DATA | dynamical system | Models | Analysis | Genes | Differential equations

Dynamical system | System of piecewise linear differential equations | Gene regulation | Optimization problem | Computational biology | computational biology | optimization problem | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | gene regulation | system of piecewise linear differential equations | PROBABILISTIC BOOLEAN NETWORKS | EXPRESSION DATA | dynamical system | Models | Analysis | Genes | Differential equations

Journal Article

Information Sciences, ISSN 0020-0255, 10/2014, Volume 281, pp. 53 - 65

In a recent seminal paper, Rudeanu derived necessary and sufficient conditions for the most general form of the subsumptive general solution of a Boolean...

Boolean equation | Subsumptive general solution | Rudeanu | Don’t care | Eliminant | Complete sum | Don't care | MINIMIZATION | ENTERED KARNAUGH MAPS | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | PRIME IMPLICANTS | Trees | Frames | Algebra | Mathematical analysis | Generators | Mathematical models | Boolean algebra | Representations

Boolean equation | Subsumptive general solution | Rudeanu | Don’t care | Eliminant | Complete sum | Don't care | MINIMIZATION | ENTERED KARNAUGH MAPS | COMPUTER SCIENCE, INFORMATION SYSTEMS | SYSTEMS | PRIME IMPLICANTS | Trees | Frames | Algebra | Mathematical analysis | Generators | Mathematical models | Boolean algebra | Representations

Journal Article

Journal of Theoretical Biology, ISSN 0022-5193, 2008, Volume 255, Issue 3, pp. 269 - 277

Methods for modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without much closer...

Gene regulatory networks | Fission yeast | Computer simulations | Boolean networks | Differential equations | Cell cycle | SIGNALING PATHWAYS | DROSOPHILA-MELANOGASTER | GENETIC-CONTROL | DIVISION CYCLE | COUPLED CHEMICAL-REACTIONS | CIRCUITS | YEAST-CELL-CYCLE | LOGICAL ANALYSIS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Cell Cycle - genetics | Yeasts - genetics | Gene Expression Profiling - statistics & numerical data | Computer Simulation | Models, Genetic | Models, Statistical | Gene Regulatory Networks

Gene regulatory networks | Fission yeast | Computer simulations | Boolean networks | Differential equations | Cell cycle | SIGNALING PATHWAYS | DROSOPHILA-MELANOGASTER | GENETIC-CONTROL | DIVISION CYCLE | COUPLED CHEMICAL-REACTIONS | CIRCUITS | YEAST-CELL-CYCLE | LOGICAL ANALYSIS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | DYNAMICS | Cell Cycle - genetics | Yeasts - genetics | Gene Expression Profiling - statistics & numerical data | Computer Simulation | Models, Genetic | Models, Statistical | Gene Regulatory Networks

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 04/2015, Volume 61, Issue 4, pp. 2200 - 2209

S-boxes having large number of linearly independent multivariate biaffine or quadratic equations may be susceptible to certain kinds of algebraic attacks. In a...

Ciphers | Quadratic equations | Boolean functions | Algebraic attacks | S-box | Vectors | Polynomials | Mathematical model | Time complexity | Bi-affine equations | Power mapping | OVERDEFINED SYSTEMS | quadratic equations | algebraic attacks | COMPUTER SCIENCE, INFORMATION SYSTEMS | BLOCK CIPHERS | CRYPTANALYSIS | power mapping | AES | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Mathematical models | Equations, Quadratic | Innovations

Ciphers | Quadratic equations | Boolean functions | Algebraic attacks | S-box | Vectors | Polynomials | Mathematical model | Time complexity | Bi-affine equations | Power mapping | OVERDEFINED SYSTEMS | quadratic equations | algebraic attacks | COMPUTER SCIENCE, INFORMATION SYSTEMS | BLOCK CIPHERS | CRYPTANALYSIS | power mapping | AES | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Mathematical models | Equations, Quadratic | Innovations

Journal Article

1990, ISBN 0792391217, xviii, 273

Book

International Journal of Bifurcation and Chaos, ISSN 0218-1274, 12/2011, Volume 21, Issue 12, pp. 3511 - 3548

We study damage propagation in networks, with an emphasis on production-chain models. The models are formulated as systems of Boolean delay equations. This...

natural disasters | random graph | production chains | Damage propagation | directed graph | MULTIDISCIPLINARY SCIENCES | TELECONNECTIONS | COLLIDING CASCADES | ATMOSPHERE | INPUT-OUTPUT MODEL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NORTHERN-HEMISPHERE | DYNAMICS | OSCILLATIONS | Collapse | Economics | Networks | Mathematical analysis | Mathematical models | Boolean algebra | Damage | Delay | Economics and Finance | Humanities and Social Sciences | Environmental Sciences

natural disasters | random graph | production chains | Damage propagation | directed graph | MULTIDISCIPLINARY SCIENCES | TELECONNECTIONS | COLLIDING CASCADES | ATMOSPHERE | INPUT-OUTPUT MODEL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | NORTHERN-HEMISPHERE | DYNAMICS | OSCILLATIONS | Collapse | Economics | Networks | Mathematical analysis | Mathematical models | Boolean algebra | Damage | Delay | Economics and Finance | Humanities and Social Sciences | Environmental Sciences

Journal Article

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 2, pp. 183 - 196

In this paper we provide procedures for testing the existence of various types of generalized inverses in involutive residuated semigroups and involutive...

Mathematical procedures | Binary relations | Algebra | Semigroups | Mathematical functions | Mathematical rings | Linear equations | Residuation | Solvability | Boolean algebras | Fuzzy matrices | Involutive quantale | Fuzzy relations | Generalized inverses | Gelfand quantales | Moore-penrose equations | Residuated function | fuzzy matrices | MATHEMATICS, APPLIED | BISIMULATIONS | AUTOMATA | INEQUALITIES | REGULAR FUZZY EQUIVALENCES | involutive quantale | generalized inverses | MATHEMATICS | Moore-Penrose equations | fuzzy relations

Mathematical procedures | Binary relations | Algebra | Semigroups | Mathematical functions | Mathematical rings | Linear equations | Residuation | Solvability | Boolean algebras | Fuzzy matrices | Involutive quantale | Fuzzy relations | Generalized inverses | Gelfand quantales | Moore-penrose equations | Residuated function | fuzzy matrices | MATHEMATICS, APPLIED | BISIMULATIONS | AUTOMATA | INEQUALITIES | REGULAR FUZZY EQUIVALENCES | involutive quantale | generalized inverses | MATHEMATICS | Moore-Penrose equations | fuzzy relations

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2005, Volume 343, Issue 3, pp. 332 - 369

Boolean equation system are a useful tool for verifying formulas from modal μ -calculus on transition systems (see [Mader, Lecture Notes in Computer Science,...

Parameterised boolean equation systems | Model checking | Infinite state systems | First order modal [formula omitted]-calculus | First order modal μ | calculus | First order modal μ-calculus | MODEL-CHECKING | COMPUTER SCIENCE, THEORY & METHODS | model checking | first order modal mu-calculus | infinite state systems | parameterised boolean equation systems | Computer science

Parameterised boolean equation systems | Model checking | Infinite state systems | First order modal [formula omitted]-calculus | First order modal μ | calculus | First order modal μ-calculus | MODEL-CHECKING | COMPUTER SCIENCE, THEORY & METHODS | model checking | first order modal mu-calculus | infinite state systems | parameterised boolean equation systems | Computer science

Journal Article

Information Sciences, ISSN 0020-0255, 2010, Volume 180, Issue 12, pp. 2487 - 2497

We present a study, in a fuzzy logic framework, of the fuzzy implication operations involved in the iterative Boolean-like law I ( x , I ( x , y ) ) = I ( x ,...

T-norms | Strong negations | Iterative Boolean-like laws | T-conorms | D-implications | D-operations | COMPUTER SCIENCE, INFORMATION SYSTEMS | QL-IMPLICATIONS | Bulging | Fuzzy logic | Fuzzy set theory | Law | Fuzzy | Mathematical analysis

T-norms | Strong negations | Iterative Boolean-like laws | T-conorms | D-implications | D-operations | COMPUTER SCIENCE, INFORMATION SYSTEMS | QL-IMPLICATIONS | Bulging | Fuzzy logic | Fuzzy set theory | Law | Fuzzy | Mathematical analysis

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 5/2013, Volume 53, Issue 5, pp. 632 - 639

Systems of Boolean equations are considered. The order of maximal consistent subsystems is estimated in the general and “typical” (in a probability sense)...

Computational Mathematics and Numerical Analysis | Mathematics | Boolean system | generalized solution | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Studies | Theorems | Computational mathematics | Mathematical models | Physics | Boolean algebra | Computation | Mathematical analysis

Computational Mathematics and Numerical Analysis | Mathematics | Boolean system | generalized solution | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | Studies | Theorems | Computational mathematics | Mathematical models | Physics | Boolean algebra | Computation | Mathematical analysis

Journal Article

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