Showing papers on "Disjunctive normal form published in 2009"

Indexing Boolean expressions

Abstract: We consider the problem of efficiently indexing Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) Boolean expressions over a high-dimensional multi-valued attribute space. The goal is to rapidly find the set of Boolean expressions that evaluate to true for a given assignment of values to attributes. A solution to this problem has applications in online advertising (where a Boolean expression represents an advertiser's user targeting requirements, and an assignment of values to attributes represents the characteristics of a user visiting an online page) and in general any publish/subscribe system (where a Boolean expression represents a subscription, and an assignment of values to attributes represents an event). All existing solutions that we are aware of can only index a specialized sub-set of conjunctive and/or disjunctive expressions, and cannot efficiently handle general DNF and CNF expressions (including NOTs) over multi-valued attributes.In this paper, we present a novel solution based on the inverted list data structure that enables us to index arbitrarily complex DNF and CNF Boolean expressions over multi-valued attributes. An interesting aspect of our solution is that, by virtue of leveraging inverted lists traditionally used for ranked information retrieval, we can efficiently return the top-N matching Boolean expressions. This capability enables emerging applications such as ranked publish/subscribe systems [16], where only the top subscriptions that match an event are desired. For example, in online advertising there is a limit on the number of advertisements that can be shown on a given page and only the "best" advertisements can be displayed. We have evaluated our proposed technique based on data from an online advertising application, and the results show a dramatic performance improvement over prior techniques.

A conformant planner with explicit disjunctive representation of belief states

Abstract: This paper describes a novel and competitive complete conformant planner. Key to the enhanced performance is an efficient encoding of belief states as disjunctive normal form formulae and an efficient procedure for computing the successor belief state. We provide experimental comparative evaluation on a large pool of benchmarks. The novel design provides great efficiency and enhanced scalability, along with the intuitive structure of disjunctive normal form representations.

Polynomial functions over bounded distributive lattices

Abstract: Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and meets. Moreover, we discuss the disjunctive normal form representations of these polynomial functions.

A Space Hierarchy for k-DNF Resolution

Abstract: The k-DNF resolution proof systems are a family of systems indexed by the integer k, where the k th member is restricted to operating with formulas in disjunctive normal form with all terms of bounded arity k (k-DNF formulas). This family was introduced in (Kraj´ icek 2001) as an extension of the well- studied resolution proof system. A number of lower bounds have been proven onk-DNF resolution proof length and space, and it has also been shown that (k+1)-DNF resolution is exponentially more powerful than k-DNF resolution for all k with respect to length. For proof space, however, no corresponding hierarchy has been known except for the (very weak) subsystems restricted to tree-like proofs. In this work, we establish a strict space hierarchy for the general, unrestricted k-DNF resolution proof systems.

On detecting faults for Boolean expressions

Abstract: Fault based testing aims at detecting hypothesized faults based on specifications or program source. There are some fault based techniques for testing Boolean expressions which are commonly used to model conditions in specifications as well as logical decisions in program source. The MUMCUT strategy has been proposed to generate test cases from Boolean expressions. Moreover, it detects eight common types of hypothesized faults provided that the original expression is in irredundant disjunctive normal form, IDNF. Software practitioners are more likely to write the conditions and logical decisions in general form rather than IDNF. Hence, it is interesting to investigate the fault detecting capability of the MUMCUT strategy with respect to general form Boolean expressions. In this article, we perform empirical studies to investigate the fault detection capability of the MUMCUT strategy with respect to general form Boolean expressions as well as mutated expressions. A mutated expression can be obtained from the original given Boolean expression by making a syntactic change based on a particular type of fault.

Feature selection for medical dataset using rough set theory

Abstract: Rough set approach has been recognized to be one of the powerful tools in medical feature selection. Many feature selection methods based on rough set have been proposed, where numerous experimental results have demonstrated that these methods based on discernibility matrix are efficient. However, the high storage space and the time-consuming computation restrict its application. In this paper, we propose an efficient algorithm called as Feature Forest algorithm for generation of the reducts of a medical dataset. In the algorithm, the given dataset is transformed into a forest to form discernibility string that is the concatenation of some of features and the disjunctive normal form is computed to reduct features based on feature forest. In addition, experimental results on different datasets show that the algorithms of this paper can efficiently reduce storage cost and be computationally inexpensive.

On the Asymptotic Behavior of

Abstract: Fuzzy cellular automata (FCA) are continuous cellular automata where the local rule is defined as the “fuzzification” of the local rule of a corresponding Boolean cellular automaton in disjunctive normal form. In this paper we consider circular FCA; their asymptotic behavior has been observed through simulations and FCA have been empirically classified accordingly. No analytical study exists so far to support those observations. now start the analytical study of circular FCA’s dynamics by considering a particular set of FCA (Weighted Average rules) which includes rules displaying most of the observed dynamics, and we precisely derive their behavior. We confirm the empirical observations proving that all weighted average rules are periodic in time and space, and we derive their periods.

Uniform Interpolation for $\mathcal{ALC}$ Revisited

Abstract: The notion of uniform interpolation for description logic $\mathcal{ALC}$ has been introduced in [9]. In this paper, we reformulate the uniform interpolation for $\mathcal{ALC}$ from the angle of forgetting and show that it satisfies all desired properties of forgetting. Then we introduce an algorithm for computing the result of forgetting in concept descriptions. We present a detailed proof for the correctness of our algorithm using the Tableau for $\mathcal{ALC}$. Our results have been used to compute forgetting for $\mathcal{ALC}$ knowledge bases.

Functionally private approximations of negligibly-biased estimators

Abstract: We study functionally private approximations. An approximation function $g$ is {\em functionally private} with respect to $f$ if, for any input $x$, $g(x)$ reveals no more information about $x$ than $f(x)$. Our main result states that a function $f$ admits an efficiently-computable functionally private approximation $g$ if there exists an efficiently-computable and negligibly-biased estimator for $f$. Contrary to previous generic results, our theorem is more general and has a wider application reach.We provide two distinct applications of the above result to demonstrate its flexibility. In the data stream model, we provide a functionally private approximation to the $L_p$-norm estimation problem, a quintessential application in streaming, using only polylogarithmic space in the input size. The privacy guarantees rely on the use of pseudo-random {\em functions} (PRF) (a stronger cryptographic notion than pseudo-random generators) of which can be based on common cryptographic assumptions.The application of PRFs in this context appears to be novel and we expect other results to follow suit.Moreover, this is the first known functionally private streaming result for {\em any} problem. Our second application result states that every problem in some subclasses of \SP of hard counting problems admit efficient and functionally private approximation protocols. This result is based on a functionally private approximation for the \SDNF problem (or estimating the number of satisfiable truth assignments to a Boolean formula in disjunctive normal form), which is an application of our main theorem and previously known results.

On Constructing Threshold Networks for Pattern Classification

Abstract: This paper describes a method of constructing one-hidden layer feedforward linear threshold networks to represent Boolean functions (or partially-defined Boolean functions). The first step in the construction is sequential linear separation, a technique that has been used by a number of researchers [7, 11, 2]. Next, from a suitable sequence of linear separations, a threshold network is formed. The method described here results in a threshold network with one hidden layer. We compare this approach to the standard approach based on a Boolean function’s disjunctive normal form and to other approaches based on sequential linear separation [7, 11]

Attribute-Based Signatures with DNF Policies

Abstract: An attribute-based signature scheme is a signature scheme where a signer's private key is associate with an attribute set and a signature is associated with an access structure. Attribute-based signature schemes are useful to provide anonymity and access control for role-based systems and attribute-based systems where an identity of object is represented as a set of roles or attributes. In this paper, we formally define the definition of attribute-based signature schemes and propose the first efficient attribute-based signature scheme that requires constant number of pairing operations for verification where a policy is represented as a disjunctive normal form (DNF). To construct provably secure one, we introduce a new interactive assumption and prove that our construction is secure under the new interactive assumption and the random oracle model.

A heuristic approach to network hardening using attack graphs

Abstract: In defending against multi-step attacks, network hardening answers the following important question: Which vulnerabilities must be removed from a network in order to prevent attackers from compromising critical resources while minimizing the implied cost in terms of availability or administrative efforts. Existing approaches to network hardening derive a logic proposition to represent the negation of the attack goal in terms of initially satisfied security conditions. In the disjunctive normal form (DNF) of the logic proposition, each disjunction then provides a viable solution to network hardening. However, such solutions suffer from an exponential time complexity. In this thesis, we study heuristic methods for solving this important problem with reasonable complexity. We evaluate our proposed solutions through extensive experiments. The results show that our solution can achieve reasonably good network hardening results in significantly less time than the optimal solution would require. Also, for scenarios where additional cost constraints may render a perfectly secure network hardening solution impossible, we extend our heuristic methods to partial hardening solutions. Such solutions can provide best possible improvement in terms of security under given cost constraints.

FF-Based Feature Selection for Improved Classification of Medical Data

Abstract: In processing the medical data, choosing the optimal subset of features is important, not only to reduce the processing cost but also to improve the classification performance of the model built from the selected data. Rough Set method has been recognized to be one of the powerful tools in the medical feature selection. However, the high storage space and the time-consuming computation restrict its application. In this paper, we propose two new concepts: discernibility string and feature forest, and an efficient algorithm, the Feature Forest Based (FF-Based) algorithm, for generation of all reducts of a medical dataset. The algorithm consists of two phases: feature forest construction phase and disjunctive normal form computation phase. In the first phase, the discernibility strings that are the concatenation of some of features between two different cases construct the feature forest. In the second phase, the disjunctive normal form is computed to reduct features based on feature forest. The experimental results on the medical datasets of UCI machine learning repository and a real liver cirrhosis dataset show that the algorithms of this paper can efficiently reduce storage cost and improve the classification performance.

Synthesis for a Weak Real-Time Logic

Abstract: In this dissertation, we consider the specification and the controller synthesis problem for real-time systems. Our models for systems are kinds of Event-recording automata. We assume that controllers observe all the events occurring in the system and can prevent occurrences of controllable events. We study Event-recording Logic (ERL). We propose new algorithms for the model-checking and the satisfiability problems of that logic. Our algorithms are similar to some algorithms proposed for the same problems in the setting of the standard $\mu$-calculus. They also correct earlier proposed algorithms. We define disjunctive normal form formulas and we show that every formula is equivalent to a formula in disjunctive normal form. Unfortunately, ERL is rather weak and can not describe some interesting real-time properties, in particular some important properties for controllers. We define a new logic that we call WTmu. The logic WTmu is a weak real-time extension of the standard $\mu$-calculus. We present an algorithm for the model-checking problem of WTmu. We consider a fragment of WTmu called WT\mu for control (C-WTmu). We show that the satisfiability of C-WTmu is decidable. The algorithm that we propose for deciding whether a formula of C-WTmu, has a model does not need to know the maximal constant used in models and it enables the construction of a witness model. Using C-WTmu, we present algorithms for a centralised controller synthesis problem and a centralised $\Delta$-controller synthesis problems. The construction of witness controllers is effective.

A Non-recursive Algorithm for Solving All Attribute Reductions

Abstract: Based on the Boolean matrix in literature [3], the paper puts forward a non-recursive algorithm to change conjunctive normal form into disjunctive normal form, thus all attribute reductions are obtained. The algorithm can reduce the superfluous ones when generate conjunctive terms of disjunctive normal form, and can improve spatial and time efficiency. The algorithm is already debugged successfully under Visual C++ 6.0, and experiments prove that the method is very simple and effective.

nfn2dlp and nfnsolve: Normal Form Nested Programs Compiler and Solver

Abstract: Normal Form Nested (NFN ) programs have recently been introduced in order to allow for enriching the syntax of disjunctive logic programs under the answer sets semantics. In particular, heads of rules can be disjunctions of conjunctions, while bodies can be conjunctions of disjunctions. Different to many other proposals of this kind, NFN programs may contain variables, and a notion of safety has been defined for guaranteeing domain independence. Moreover, NFN programs can be efficiently translated to standard disjunctive logic programs (DLP ). In this paper we present the tool nfn2dlp , a compiler for NFN programs, which implements an efficient translation from safe NFN programs to safe DLP programs. The answer sets of the original NFN program can be obtained from the answer sets of the transformed program (which in turn can be obtained by using a DLP system) by a simple transformation. The system has been implemented using the object-oriented programming language Ruby and Treetop, a language for Parsing Expression Grammars (PEGs). It currently produces DLP programs in the format of DLV. The separate script nfnsolve uses DLV as a back-end to compute answer sets for NFN programs. Thus, combining the two tools we obtain a system which supports the powerful NFN language, and is available for experiments.

Computing minimal models by positively minimal disjuncts

Abstract: In this paper, we consider a method of computing minimal models in propositional logic. We firstly show that positively minimal disjuncts in DNF (Disjunctive Normal Form) of the original axiom corresponds with minimal models. A disjunct D is positively minimal if there is no disjunct which contains less positive literal than D. We show that using superset query and membership query which were used in some learning algorithms in computational learning theory, we can compute all the minimal models. We then give a restriction and an extension of the method. The restriction is to consider a class of positive (sometimes called monotone) formula where minimization corresponds with diagnosis and other important problems in computer science. Then, we can replace superset query with sampling to give an approximation method. The algorithm itself has been already proposed by [Valiant84], but we show that the algorithm can be used to approximate a set of minimal models as well. On the other hand, the extension is to consider circumscription with varied propositions. We show that we can compute equivalent formula of circumscription using a similar technique to the above.

A Recursive Algorithm of All Attribute Reductions Based on Boolean Matrix

Abstract: Based on the Boolean matrix in literature, the paper put forward a recursive algorithm to change conjunctive normal form into disjunctive normal form, thus get all attribute reductions. Experiment proves that the spatial and time efficiency of this method is higher than the ones in literature.

SoC functional intellectual property diagnosis

Abstract: The diagnosis methods of digital system on a chip, based on the disjunctive normal form, which is represented by fault coverage matrix of test sequences are proposed. The method is focused on the built-in-service functionality, presented by F-IP modules. Strategy of check-points choice which is directed on search of multiple faults in the system functionality in real time is considered.

ON THE SIZE OF A MINIMAL VERTEX COVER IN A RANDOM SUBGRAPH OF THE n-CUBE

Abstract: We describe and analyze a construction of a vertex cover (consisting of subcubes) in a random subgraph of the n-cube. The main idea of the construction is to select subcubes with minimal intersection into the vertex cover. We estimate the upper bound of such a vertex cover. Our analysis gives a theoretical justification for a heuristic that minimizes the disjunctive normal form of a random Boolean function by selecting conjunctions according to the strategy of minimal intersections. Mathematics Subject Classification 2000: 05C80, 05C70