Boolean Variables Research Articles

RQL: A Query Language for Rule Discovery in Databases

Promoting declarative approaches in data mining is a long standing theme, the main idea being to simplify as much as possible the way data analysts interact with their data. This paper goes into this direction by proposing a well-founded logical query language, SafeRL, allowing the expression of a wide variety of rules to be discovered against a database. By rules, we mean statements of the form “if …then …”, as defined in logics for “implications” between boolean variables. As a consequence, SafeRL extends and generalizes functional dependencies to new and unexpected rules. We provide a query rewriting technique and a constructive proof of the main query equivalence theorem, leading to an efficient query processing technique. From SafeRL, we have devised RQL, a user-friendly SQL-like query language. We have shown how a tight integration can be performed on top of any relational database management system. Every RQL query turns out to be seen as a query processing problem, instead of a particular rule mining problem. This approach has been implemented and experimented on sensor network data. A web prototype has been released and is freely available (http://rql.insa-lyon.fr). Data analysts can upload a sample of their data, write their own RQL queries and get answers to know whether or not a rule holds (if not, a counterexample from the database is displayed) and much more.

DELIVERY OF GOODS TO THE RAILWAY NETWORK WITH REGARD TO CAPACITY AS DISTILLERIES VECTOR OPTIMIZATION PROBLEMS

The aim of this work is to develop a mathematical model of the organization of the vagonopotokov in freight trains based vector optimization-based passenger transportation services and restrictions on capacity spans. The main objective of the study is the distribution of freight and passenger poezdopotokov on the railway network, taking into account capacity constraints spans. The object of research is the railway network polygon with vertices at the service station. The subject of study is the distribution of passenger and freight poezdopotokov on the rail network. The method of research is the theory of multiple functions and vector optimization-tion. Scientific novelty is to provide a new method for solving problems such as backpack, which can be used in the calculation of the plan of forming single-group of through trains and eliminates the Boolean variables and solve for ordinary cottage-optimization Lagrange multipliers.

A general framework for static profiling of parametric resource usage

AbstractFor some applications, standard resource analyses do not provide the information required. Such analyses estimate the total resource usage of a program (without executing it) as functions on input data sizes. However, some applications require knowing how such total resource usage is distributed over selected parts of a program. We propose a novel, general, and flexible framework for setting up cost equations/relations which can be instantiated for performing a wide range of resource usage analyses, including both static profiling and the inference of the standard notion of cost. We extend and generalize standard resource analysis techniques, so that the relations generated include additional Boolean control variables for switching on or off different terms in the relations, as required by the desired resource usage profile. We also instantiate our framework to perform static profiling of accumulated cost (also parameterized by input data sizes). Such information is much more useful to the software developer than the standard notion of cost: it identifies the parts of the program that have the greatest impact on the total program cost, and which therefore should be optimized first. We also report on an implementation of our framework within the CiaoPP system, and its instantiation for accumulated cost, and provide some experimental results. In addition to generality, our new method brings important advantages over our previous approach based on a program transformation, including support for non-deterministic programs, better and easier integration in the compiler, and higher efficiency.

Safety assessment for the ultimate heat sink (UHS) system with non-injection concept in nuclear power plants (NPPs)

ABSTRACTFollowing the Fukushima accident, it is proposed to find a better safety system, which has a pool-type cooling system without coolant injections. Since the conventional piping-based injection systems have failed in treating the three major severe accidents, the artificial pool could be constructed to cover the failed reactor core systems in which the pool-like structure is constructed. Regarding this study, there were some previous studies about the ultimate heat sink (UHS). In this study, the system dynamics (SD) modeling is performed in the case of Fukushima Unit 1 accident. The basic events are obtained by the Boolean values as 0 and 1. The quantifications are obtained by the SD algorithm incorporated with the Vensim software. In the simulations work, there is a plateau region between the 25th and 45th years in the interested period. The nonlinear algorithm is applied for the UHS analysis which was not installed for the commercial use yet.

On the phase transitions of (k, q)-SAT

Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let Tk(V) denote the set of all 2knk possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in Tk(V) independently with probability p, and let Q be a given set of q “bad” tuple assignments. An instance I = (C,Q) is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tuple assignment in Q. Suppose that θ, q > 0 are fixed and e = e(n) > 0 be such that elnn/lnlnn→∞. Let k ≥ (1 + θ) log2n and let \({p_0} = \frac{{\ln 2}}{{q{n^{k - 1}}}}\). We prove that $$\mathop {\lim }\limits_{n \to \infty } P\left[ {I is satisfiable} \right] = \left\{ {\begin{array}{*{20}c} {1,} & {p \leqslant (1 - \varepsilon )p_0 ,} \\ {0,} & {p \geqslant (1 + \varepsilon )p_0 .} \\ \end{array} } \right.$$

Development of an ecomomic and mathematical model of loading a freight and passenger ferry

Ferries are an important structural element of the ferry transport technological system (TTS) and an integral part of the global navigation. Today, ferry transportation is widespread in Europe, the Baltics and the CIS countries. The most developed traffic on the maritime market is such freight and passenger ferries as ro-ro passenger and ro-pax ferries. Ferries are a linear fleet with a number of peculiarities that complicate the decision-making process on the formation of their loading. The features that do not depend on the ferry sailing region include diversified cargos, a composite cargo and passenger loading, a multitude of consignments from different shippers, a wide variety of tariffs, discounts and surcharges for transportation depending on many factors, and a set schedule of the ferry operation. The study presents an economic and mathematical model that maximally takes into account the specific features of organizing ferry transportation as well as the technical and operational characteristics of vessels. This is achieved by incorporating into the model structure those restrictions whose left side reflects the characteristics of the ferry and the line, whereas the right side reveals the parameters of the cargo and passenger traffic. In particular, it should be specified that a composite loading of the ferry with both cargos and passengers implies restrictions that prevent the carriage of passengers without a cargo or transporting cargos without passengers accompanying them. This peculiarity of ferry loading was disregarded in previous studies devoted to optimizing the loading of vessels. Furthermore, the control parameters, which are Boolean variables, used in the model help take into account the linear and mass characteristics of each cargo unit, which is caused by a wide variety of cargos within the same nomenclature. The specified peculiarities of the suggested economic and mathematical model make it applicable for both Ukrainian and foreign ferry operators. Furthermore, the model is open to any, if necessary, modifications depending on the requirements of individual companies due to addition or elimination of certain restrictions.

Mathematical model of selecting the elements of weather monitoring system for highway

Analyzes of approaches and methods of synthesis of intelligent transport systems are conducted. The implementation of intelligent transport systems will improve traffic management safety, provide reliable transportation and preservation of vehicles and cargo, and improve environmental protection. For prompt consideration of the impact of meteorological factors it should be used a system of meteorological service that will quickly decide on necessary actions in a particular stretch of road. Mathematical model of selecting the elements of weather monitoring system for highway were developed. The model refers to problems of discrete programming with Boolean variables, for their implementation it is proposed to use: for the tasks of small dimension – exhaustive search of options; for the tasks of large dimension – the method of random search. An example of selecting the elements of weather monitoring system was considered. The prospect of further research is to develop software that will automate the process of synthesis of intelligent transport systems.

Assessment of the small modular reactor (SMR) marketing using modified network dynamics-based system dynamics (SD) method

ABSTRACTFollowing the export success of the South Korean small modular reactor (SMR), it has been investigated for the marketing strategy of nuclear power plants (NPPs). The information feedback oriented method for the social-business matters, system dynamics (SD), is applied to the assessment of the marketing strategy in which the forecasting skills are performed. Each element has the Boolean value as 0 or 1 in which the values are selected by the random number generation. If the generated values are higher than the designed value decided by the operator, it is 1. Otherwise, it is 0. The networking based dynamical modeling is discussed. The modification of the linear networking is changed by the SD algorithm where the feedback and multiple connections are added to the original network dynamics theory. This new method has shown the complexity of the marketing strategy, especially for the NPPs.

Order-to-chaos transition in the hardness of random Boolean satisfiability problems.

Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k-SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ, an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N, the hardness of formulas in random k-SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α, hardness appears through a second-order phase transition at α_{χ} in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ∼N^{B|α-α_{χ}|^{1-γ}} with 0<γ<1. We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.

Minimal Conjunctive Normal Expression of Continuous Piecewise Affine Functions

Continuous piecewise affine (PWA) functions arise in many aspects of control. For this kind of function, we propose the minimal conjunctive normal expression (CNE). The CNE can be expressed as the minimum of a collection of terms, each of which is the maximum of a set of affine functions. The minimal CNE is defined to contain the smallest number of parameters. Analogous to Boolean algebra, we propose implicants and prime implicants for continuous PWA functions. After obtaining all prime implicants, the problem of finding minimal CNEs can then be cast as a binary programming problem. A sharp bound on the number of boolean variables in the binary programming problem is given. In two worked examples, minimal CNEs are derived for given continuous PWA functions.

An algebraic approach for detecting nearly dangerous situations in expert systems

The aim of this work is to present theoretically a new algebraic method for detecting nearly dangerous states in an expert system whose knowledge is represented by propositional Boolean logic. Given a dangerous state which does not happen at present, our method is able to detect if a dangerous situation would happen if an input variable of the Expert System changed. The method presented here is based on calculating just one Groebner basis of a polynomial ideal representing the system knowledge. In this way, although the Expert System is designed to notify only dangerous situations, we have developed an algebraic model for including in the expert system the ability to recommend watching carefully some Boolean variables such that if one of them changed, the system would fall in a dangerous situation. In this way, the same expert system not only warns about dangerous situations but also about nearly dangerous situations. It may be noted that our method does not require to change the Expert System for including this facility. As far as our knowledge goes, our work is completely new in the field of Expert Systems.

On discovering co-location patterns in datasets: a case study of pollutants and child cancers

We intend to identify relationships between cancer cases and pollutant emissions and attempt to understand whether cancer in children is typically located together with some specific chemical combinations or is independent. Co-location pattern analysis seems to be the appropriate investigation to perform. Co-location mining is one of the tasks of spatial data mining which focuses on the detection of co-location patterns, the sets of spatial features frequently located in close proximity of each other. Most previous works are based on transaction-free apriori-like algorithms which are dependent on user-defined thresholds and are designed for boolean data points. Due to the absence of a clear notion of transactions, it is nontrivial to use association rule mining techniques to tackle the co-location mining problem. The approach we propose is based on a grid "transactionization" of the geographic space and is designed to mine datasets with extended spatial objects. Uncertainty of the feature presence in transactions is taken into account in our model. The statistical test is used instead of global thresholds to detect significant co-location patterns and rules. We evaluate our approach on synthetic and real datasets. This approach can be used by researchers looking for spatial associations between environmental and health factors. In addition, we explain the data modelling framework which is used on real datasets of pollutants (PRTR/NPRI) and childhood cancer cases.

Mining temporal roles using many-valued concepts

Many of today's access control policies are associated with temporal restrictions. Under temporal role-based access control (TRBAC), roles have an associated temporal component, which allows them to better encapsulate such temporal access control policies. However, given their complexity, TRBAC systems can only be well managed if the set of roles is correctly defined. The process of deriving an optimal set of such roles is known as temporal role mining. In this paper, we formally define the temporal role mining problem (TRMP) in the form of a matrix decomposition problem, by introducing a new operator that multiplies a set with a Boolean value and redefining existing matrix multiplication operations in terms of it. We also define a new metric for temporal role mining, called cumulative overhead of temporal roles and permissions (CO-TRAP), which takes into consideration the administrative effort required for managing the resulting TRBAC system. Since TRMP as well as minimization of CO-TRAP are NP-complete problems, we propose two greedy algorithms based on many-valued concepts. Experimental evaluation on a number of real-world datasets shows that the proposed approach is both efficient and effective.

Lattice and metric completions of the classical logic metric space and a comparison1

Based on the concept of truth degree for logical formulas, a pseudo-metric is constructed on the set of all classical propositional formulas, and a metric is naturally induced on the corresponding Lindenbaum algebra of Boolean type, which constitutes a metric space, called the classical logic metric space. We respectively study both lattice completions and metric completions of this space, and compare the two kinds of completions from the angle of lattice structure as well as metric structure. On one hand, it is proved that metric completions of the classical logic metric space are complete Boolean algebras, which also act as lattice completions of the Lindenbaum algebra. On the other hand, it is pointed out that the normal lattice completion of the Lindenbaum algebra constitutes a Boolean algebra as well, which is strictly smaller than metric completions of the classical logic metric space in the sense of order-embedding. Also, the normal lattice completion can be seen as a dense subspace of the metric completions in the sense of isometry.

Adaptive-TTCM-Aided Near-Instantaneously Adaptive Dynamic Network Coding for Cooperative Cognitive Radio Networks

An adaptive dynamic network coding (ADNC) scheme conceived for cooperative cognitive radio (CCR) is proposed for devising a novel ADNC-CCR system. The system is designed for supporting communications between multiple primary users (PUs) and a common base station (BS), where the independent source information is transmitted from the PUs to the BS with the aid of multiple cognitive users (CUs) acting as relay nodes (RNs). To facilitate the recovery of the source information at the BS, the CUs invoke the ADNC technique, which is assisted by our cooperative protocol operating by exchanging the CCR-based control information between near-instantaneously adaptive turbo trellis coded modulation (ATTCM) and network coding (NC) codec, as well as between the CUs and the BS. More particularly, near-instantaneous ATTCM is employed for appropriately adjusting both the modulation mode and the code rate of the channel coding itself and of the NC, according to the near-instantaneous channel conditions. As a result, our novel ADNC-CCR system constructed on the basis of our holistic approach is capable of providing an increased throughput, despite reducing the transmission period of the PU. This reduced transmission period can also be directly translated into an increased duration for secondary communications of the CUs. In our proposed ADNC-CCR scheme, both the PUs and CUs employ our ATTCM scheme. As an additional novelty, the network encoder may also be activated in its adaptive mode for supporting the CUs, depending on the Boolean value of the feedback flags generated based on the success/failure of the ATTCM decoder and of the network decoder, which is evaluated and fed back by the BS. Quantitatively, it was found that the joint holistic design of our ATTCM-ADNC-CCR scheme is either capable of freeing up an approximately 40% of the PU's bandwidth in comparison to its noncooperative counterpart or increasing the attainable throughput by 2 bits/symbol.

Inverted Fuzzy Implications in Approximate Reasoning

In 1973 Lotfi Zadeh introduced the theory of fuzzy logic [17]. Fuzzy logic was an extension of Boolean logic so that it allowed using not only Boolean values to express reality. One kind of basic logical operations in fuzzy logic are so-called fuzzy implications. From over eight decades a number of different fuzzy implications have been described [3] - [16]. In the family of all fuzzy implications the partial order induced from [0,1] interval exists. Pairs of incomparable fuzzy implications can generate new fuzzy implications by using min(inf) and max(sup) operations. As a result the structure of lattice is created ([1], page 186). This leads to the following question: how to choose the correct functions among basic fuzzy implications and other generated as described above. In our paper, we propose a new method for choosing implications. Our method allows to compare two fuzzy implications. If the truth value of the antecedent and the truth value of the implication are given, by means of inverse fuzzy implications we can easily optimize the truth value of the implication consequent. In other words, we can choose the fuzzy implication, which has the greatest or the smallest truth value of the implication consequent or which has greater or smaller truth value than another implication. Primary results regarding this problem are included in the paper [14].

Generalised and Quotient Models for Random And/Or Trees and Application to Satisfiability

This article is motivated by the following satisfiability question: pick uniformly at random an $$\mathsf {and/or}$$ Boolean expression of length n, built on a set of $$k_n$$ Boolean variables. What is the probability that this expression is satisfiable? asymptotically when n tends to infinity? The model of random Boolean expressions developed in the present paper is the model of Boolean Catalan trees, already extensively studied in the literature for a constant sequence $$(k_n)_{n\ge 1}$$ . The fundamental breakthrough of this paper is to generalise the previous results for any (reasonable) sequence of integers $$(k_n)_{n\ge 1}$$ , which enables us, in particular, to solve the above satisfiability question. We also analyse the effect of introducing a natural equivalence relation on the set of Boolean expressions. This new quotient model happens to exhibit a very interesting threshold (or saturation) phenomena at $$k_n = {n}\big /{\ln n}$$ .

An Experiment with Satisfiability Modulo SAT

In recent years, the approach of satisfiability modulo theories (SMT) has been very successful in solving many constraint satisfaction problems. In a typical SMT solver, the base constraints are expressed as a set of propositional clauses, where each Boolean variable is an abstraction of an atomic formula of first-order logic and the interpretation of the formula is constrained by a background theory. A widely studied theory is the linear pseudo-Boolean logic. Following this approach, we present an experiment of a SMT solver where the background theory can be specified in propositional logic and implemented by a procedure. We chose such a procedural background theory because we found no better ways to attack a previously open problem in combinatorial design, i.e., the existence of diagonally ordered magic squares of all orders.

A Complete Dichotomy Rises from the Capture of Vanishing Signatures

We prove a complexity dichotomy theorem for Holant problems over an arbitrary set of complex-valued symmetric constraint functions $\mathcal{F}$ on Boolean variables. This extends and unifies all previous dichotomies for Holant problems on symmetric constraint functions (taking values without a finite modulus). We define and characterize all symmetric vanishing signatures; they turn out to be essential to the complete classification of Holant problems. The dichotomy theorem has an explicit tractability criterion expressible in terms of holographic transformations. A Holant problem defined by a set of constraint functions $\mathcal{F}$ is solvable in polynomial time if it satisfies this tractability criterion, and is #P-hard otherwise. The tractability criterion can be intuitively stated as follows: A set $\mathcal{F}$ is tractable if (1) every function in $\mathcal{F}$ has arity at most two; or (2) $\mathcal{F}$ is transformable to an affine type; or (3) $\mathcal{F}$ is transformable to a product type; o...

Boolean Differentiation Equations Applicable in Reconfigurable Computational Medium

High performance computing environment synthesis with parallel architecture reconstructing throughout the process itself is described. Synthesized computational medium involving Boolean differential equation calculations so as to function in real-time image processing. Automaton imaging was illustrated involving the rearrangement of every processing medium element to calculate the partial differentials of n-th order in respect to Boolean function variables. The method of obtaining setting codes for each element was also described. An example in calculating 2 nd -order Boolean derivative to two differentials in respect to Boolean functions, depending on three arguments within the reconstructible computational medium of 8×8 processing elements was given.