Prime Implicants Research Articles

Increasing Intergroup Cooperation Toward Social Change by Restoring Advantaged and Disadvantaged Groups’ Positive Identities

In this article, we develop a perspective on social change as cooperation between advantaged and disadvantaged groups to facilitate not only redistribution of power and wealth but also restoration of threatened identity dimensions. We argue that disadvantaged groups experience threats to their agency whereas advantaged groups experience threats to their morality. Restoration of these aspects of groups’ identities can unlock the potential for collective action among members of disadvantaged groups and for a greater willingness to change the status quo toward equality among members of advantaged groups. A major theoretical implication of these findings is that social psychological theorizing should pay greater attention to morally based motivations as critical factors in the facilitation of change. A prime practical implication is that interventions designed to improve intergroup relations should consider not only acceptance-related but also agency-related motivations (e.g., through a “common stigmatizers identity” re-categorization strategy).

Narratives and Goals

Goals are a central feature of narratives, and, thus, narratives may be particularly potent means of goal priming. Two studies examined two features of goal priming (postdelay behavioral assimilation and postfulfillment accessibility) that have been theorized to distinguish goal from semantic construct priming. Across the studies, participants were primed with high achievement, either in a narrative or nonnarrative context and then completed either a behavioral task, followed by a measure of construct accessibility, or a behavioral task after a delay. Indicative of goal priming, narrative-primed participants showed greater postdelay behavioral assimilation and less postfulfillment accessibility than those exposed to the nonnarrative prime. The implications of goal priming from narratives are discussed in relation to both theoretical and methodological issues.

A Boolean theory of signatures for tonal scales

We explore the concept of tonal signatures developed and put into musical practice by one of us (Mezzadri). A tonal signature of a scale S is a minimal subset of notes within S that is not contained in any scale S′ different from S. We present a set covering model to find a smallest signature. We also show that the signatures of a scale are the prime implicants of a suitable monotone Boolean function represented by a Conjunctive Normal Form. On this ground, we introduce a more general notion of Boolean signature, depending on a Boolean operator. The computational machinery for generating Boolean signatures remains essentially the same. The richness and variety of Boolean signatures has a great potential for the development of new paradigms in polytonal harmony.

Boolean functions with long prime implicants

In this short note we introduce a hierarchy of classes of Boolean functions, where each class is defined by the minimum allowed length of prime implicants of the functions in the class. We show that for a given DNF and a given class in the hierarchy, it is possible to test in polynomial time whether the DNF represents a function from the given class. For the first class in the hierarchy we moreover present a polynomial time algorithm which for a given input DNF outputs a shortest logically equivalent DNF, i.e. a shortest DNF representation of the underlying function. This class is therefore a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. For the second class and higher classes in the hierarchy we show that the Boolean minimization problem can be approximated within a constant factor.

Prime and Essential Prime Implicants of Boolean Functions through Cubical Representation

K Maps are generally and ideally , thought to be simplest form for obtaining solution of Boolean equations.Cubical Representation of Boolean equations is an alternate pick to incur a solution, otherwise to be meted out with Truth Tables, Boolean Laws and different traits of Karnaugh Maps. Largest possible k- cubes that exist for a given function are equivalent to its prime implicants. A technique of minimization of Logic functions is tried to be achieved through cubical methods. The main purpose is to make aware and utilise the advantages of cubical techniques in minimization of Logic functions. All this is done with an aim to achieve minimal cost solution.

Implementing dynamic flowgraph methodology models with logic programs

The dynamic flowgraph methodology is a promising way to find the prime implicants of a top event for a dynamic system possibly containing digital subsystems. This article demonstrates how to express dynamic flowgraph methodology models as logic programs, and top events as queries to those programs, in a natural and comprehensible way. Computation of the logic program lists the prime implicants of a top event in the system. We also present and implement an algorithm for computing the probability of the top event from its prime implicants. Together, computation of prime implicants and calculation of top event probability from these constitute a complete way of finding a system’s failure probability. Logic programs, implemented in this article in the leading logic programming language Prolog, enable rapid prototyping of dynamic flowgraph methodology models. The logic programming framework introduced here could also be utilized in teaching dynamic flowgraph methodology in risk analysis courses.

Derivations of Single Hypothetical Don't-Care Minterms Using the Quasi Quine-McCluskey Method

Automatically deriving only individual dont-care minterms that can effectively reduce a Boolean logic expressions are being investigated. Dont-care conditions play an important role in optimizing logic design. The type of unknown dont-care minterms that can always reduce the number of product terms in Boolean expression are referred as single hypothetical dont-care (S-HDC) minterms. This paper describes the Quasi Quine-McCluskey method that systematically derives S-HDC minterms. For the most part, this method is similar to the original Quine-McCluskey method in deriving the prime implicants. However, the Quasi Quine-McCluskey method further derives S-HDC minterms by applying so-called a combinatorial comparison operation. Upon completion of the procedure, the designer can review generated S-HDC minterms to test its appropriateness for a particular application.

Effects of subliminal hints on insight problem solving

Two experiments tested a total of 509 participants on insight problems (the radiation problem and the nine-dot problem). Half of the participants were first exposed to a 1-min movie that included a subliminal hint. The hint raised the solution rate of people who did not recognize it. In addition, the way they solved the problem was affected by the hint. In Experiment 3, a novel technique was introduced to address some methodological concerns raised by Experiments 1 and 2. A total of 80 participants solved the 10-coin problem, and half of them were exposed to a subliminal hint. The hint facilitated solving the problem, and it shortened the solution time. Some implications of subliminal priming for research on and theorizing about insight problem solving are discussed.

Solving dynamic flowgraph methodology models using binary decision diagrams

Dynamic flowgraph methodology (DFM) is a computationally challenging approach to the reliability analysis of dynamic systems with feedback loops. To improve the computational efficiency of DFM modelling, we propose a new approach, based on binary decision diagrams (BDDs), to solving DFM models. The objective of DFM analysis is to identify the root causes of a postulated top event. The result is a set of prime implicants that represent system faults resulting from diverse combinations of software logic errors, hardware failures, human errors and adverse environmental conditions. Two approaches to solving prime implicants have been implemented in software called YADRAT. The first approach is based on meta-products, and the second on zero-suppressed BDDs (ZBDD). Both approaches have been used previously in fault tree analysis. In this work, the ideas of prime implicant computations are adapted to a dynamic reliability analysis approach combined with multi-valued logic. The computational efforts required for the two approaches are compared by analysing three example systems. The results of the comparison show that BDDs are applicable in DFM computation and that in particular the ZBDD-based approach can solve moderately sized DFM models in a reasonable time.

In Search of a Better Heuristic Algorithm for Simplification of Switching Function - A Challenge to ESPRESSO

Finding minimum cost switching function is a n intractable problem. The number of prime implicant of a typical switching function is of the order of 3n [5][13]. When fitness function with respect to cost is the only goal, the existing algorithms require faces combinatorial explosion [20]. The allurement of approximation and heuristic algorithms in this area has already generated ESPRESSO algorithm. We find that our algorithm presented here is at least equal or more cost effective than the ESPRESSO algorithm. The paper shows a new approach for attainment of our claim. We hope the algorithm presented here is a new attachment to the existing state of the art technology.

INFORMATION SECURITY BY BIOMETRIC WATERKING

In the recent digital world information security, person identification and authentication, and network security are the prime implications and off course requirements. To fulfill the above requirement watermarking is used widely with biometric information i.e. face image, iris, fingerprint, signature, hand geometry, voice and key stroke pattern. We propose a method for securing and protecting the biometric information of any person with the help of watermarking. The security can also be improved with the help of secrete key. Now a day’s multimodal biometric watermarking is the most advanced technology for information security where more than one biometric information’s are combined for enhancing security and privacy of information and system. In this paper we used face image as the biometric information to be secured, iris image with specific size with key is used for security improvement.

Context-dependent effects of induced resistance under co-infection in a plant-pathogen interaction.

The ability of a parasite strain to establish and grow on its host may be drastically altered by simultaneous infection by other parasite strains, and dynamics under multiple infection have been suggested to be a major force driving pathogen evolution. Here, I studied whether hosts’ induced defenses mediate dynamics of multiple infection of the fungal pathogen, Podosphaera plantaginis, infecting Plantago lanceolata. A laboratory study of sequential infections, where interaction between pathogen strains was prevented, showed that ability to establish remained unaffected, but prior infection elevates the host's resistance to the degree that subsequent infection development is significantly reduced. However, when inoculated plants and their healthy controls were planted back into their natural populations, hosts with prior infection became more heavily infected by the subsequent infections than the initially healthy plants. Hence, a controlled short-term laboratory study is a poor predictor of the host's ability to mediate multiple infection during the course of natural epidemics. These results have applied implications for priming where the plants’ defenses are elicited to provide protection against further attack, highlighting the importance of testing priming under natural conditions for relevant time scales.

Planning and Acting in Incomplete Domains

Engineering complete planning domain descriptions is often very costly because of human error or lack of domain knowl- edge. Learning complete domain descriptions is also very challenging because many features are irrelevant to achieving the goals and data may be scarce. We present a planner and agent that respectively plan and act in incomplete domains by i) synthesizing plans to avoid execution failure due to ignorance of the domain model, and ii) passively learning about the domain model during execution to improve later re-planning attempts. Our planner DeFault is the first to reason about a domain’s incompleteness to avoid potential plan failure. DeFault computes failure explanations for each action and state in the plan and counts the number of interpretations of the incomplete domain where failure will occur. We show that DeFault performs best by counting prime implicants (failure diagnoses) rather than propositional models. Our agent Goalie learns about the preconditions and effects of incompletely-specified actions while monitoring its state and, in conjunction with DeFault plan failure explanations, can diagnose past and future action failures. We show that by reasoning about incompleteness (as opposed to ignoring it) Goalie fails and re-plans less and executes fewer actions.

Fast computation of the prime implicants by exact direct-cover algorithm based on the new partial ordering operation rule

In this study, a novel OFF-set based direct-cover Exact Minimization Algorithm (EMA) is proposed for single-output Boolean functions represented in a sum-of-products form. To obtain the complete set of prime implicants covering the given Target Minterm (ON-minterm), the proposed method uses OFF-cubes (OFF-minterms) expanded by this Target Minterm. The amount of temporary results produced by this method does not exceed the size of the OFF-set. In order to achieve the goal of this study, which is to make faster computations, logic operations were used instead of the standard operations. Expansion OFF-cubes, commutative absorption operations and intersection operations are realized by logic operations for fast computation. The proposed minimization method is tested on several classes of benchmarks and then compared with the ESPRESSO algorithm. The results show that the proposed algorithm obtains more accurate and faster results than ESPRESSO does.

A Logical Study of Partial Entailment

We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means that under the circumstance of \Gamma, if P is true then some "part" of Q will also be true. We distinguish three different kinds of partial entailments and formalize them by using an extended notion of prime implicant. We study their semantic properties, which show that, surprisingly, partial entailments fail for many simple inference rules. Then, we study the related computational properties, which indicate that partial entailments are relatively difficult to be computed. Finally, we consider a potential application of partial entailments in reasoning about rational agents.

Coupling Logical Analysis of Data and Shadow Clustering for Partially Defined Positive Boolean Function Reconstruction

The problem of reconstructing the and-or expression of a partially defined positive Boolean function (pdpBf) is solved by adopting a novel algorithm, denoted by LSC, which combines the advantages of two efficient techniques, Logical Analysis of Data (LAD) and Shadow Clustering (SC). The kernel of the approach followed by LAD consists in a breadth-first enumeration of all the prime implicants whose degree is not greater than a fixed maximum d. In contrast, SC adopts an effective heuristic procedure for retrieving the most promising logical products to be included in the resulting and-or expression. Since the computational cost required by LAD prevents its application even for relatively small dimensions of the input domain, LSC employs a depth-first approach, with asymptotically linear memory occupation, to analyze the prime implicants having degree not greater than d. In addition, the theoretical analysis proves that LSC presents almost the same asymptotic time complexity as LAD. Extensive simulations on artificial benchmarks validate the good behavior of the computational cost exhibited by LSC, in agreement with the theoretical analysis. Furthermore, the pdpBf retrieved by LSC always shows a better performance, in terms of complexity and accuracy, with respect to those obtained by LAD.

ICONE19-43471 A FAST DEDUCTIVE ANALYSIS TOOLSET FOR DYNAMIC FLOWGRAPH METHODOLOGY

A fast Dynamic Flowgraph Methodology (DFM) software program has been developed, based on Binary Decision Diagram (BDD)/Zero-Suppressed BDD (ZDD) data structure and a recursive 'divide-and-conquer' approach, and using the 'Deduction Sequence Heuristic Strategy (DSHS)' and 'All-States-One-Byte Representation (ASOB)' proposed by us. Experimental results show that DSHS and ASOB are very useful for speeding up the deductive procedure and reducing total runtime. The software accelerates the speed of DFM deductive analysis and Complete Base of Prime Implicants (CBPI) derivation at least 10 times more than Dymonda for 3 or 4 steps trace back deduction analysis of the benchmark model.

McColl and Minimization

In 1952, Quine showed that the problem of reducing a propositional formula to a simplest normal equivalent can be solved in two steps, viz., (i) express the given formula, Φ, equivalently as the disjunction of all its prime implicants, and (ii) find all non-redundant disjunctions of the latter that are equivalent to Φ (Quine 1952). However, it seems not generally known that an ingenious form of the same two-step process was published by Hugh McColl in 1878.

The reliability importance of components and prime implicants in coherent and non-coherent systems including total-order interactions

In the management of complex systems, knowledge of how components contribute to system performance is essential to the correct allocation of resources. Recent works have renewed interest in the properties of the joint ( J) and differential ( D) reliability importance measures. However, a common background for these importance measures has not been developed yet. In this work, we build a unified framework for the utilization of J and D in both coherent and non-coherent systems. We show that the reliability function of any system is multilinear and its Taylor expansion is exact at an order T. We then introduce a total order importance measure ( D T ) that coincides with the exact portion of the change in system reliability associated with any (finite or infinitesimal) change in component reliabilities. We show that D T synthesizes the Birnbaum, joint and differential importance of all orders in one unique indicator. We propose an algorithm that enables the numerical estimation of D T by varying one probability at a time, making it suitable in the analysis of complex systems. Findings demonstrate that the simultaneous utilization of D T and J provides reliability analysts with a complete dissection of system performance.

Psychological Distance and Priming: When Do Semantic Primes Impact Social Evaluations?

Semantic primes influence the impressions and evaluations people form of others. According to construal level theory (CLT), as stimuli get closer psychologically (e.g., physically, probabilistically), people construe stimuli in more concrete, localized, individuating terms. Across three studies, the authors present participants with individuals performing behaviors (skydiving, motor biking) that are ambiguous with respect to being either adventurous or reckless. Using a CLT framework, the authors show that people are more likely to assimilate their judgments of others to available semantic primes for psychologically close rather than distant targets (Studies 1 and 2). Conversely, they show that general, global attitudes drive evaluations more for distant rather than close targets (Study 3). Implications for priming more broadly are discussed.