scholarly journals Satisfiability in Boolean Logic (SAT problem) is polynomial?

2021 ◽  
Vol 14 (5) ◽  
pp. 667-671
Author(s):  
Vladimir V. Rybakov ◽  
Keyword(s):  
Polynomial Algorithm ◽  
Boolean Logic ◽  
Sat Problem

We find a polynomial algorithm to solve SAT problem in Boolean Logic

scholarly journals Resolvable Networks—A Graphical Tool for Representing and Solving SAT

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2597
Author(s):  
Gábor Kusper ◽  
Csaba Biró ◽  
Benedek Nagy
Keyword(s):  
Directed Graphs ◽  
Important Application ◽  
Boolean Logic ◽  
Wireless Sensor ◽  
Incoming Edge ◽  
Sat Problem ◽  
Graphical Tool ◽  
Strongly Connected ◽  
Information Bank ◽  
Source And Sink

In this paper, we introduce the notion of resolvable networks. A resolvable network is a digraph of subnetworks, where subnetworks may overlap, and the inner structure of subnetworks are not interesting from the viewpoint of the network. There are two special subnetworks, Source and Sink, with the following properties: there is no incoming edge to Source, and there is no outgoing edge from Sink. Any resolvable network can be represented by a satisfiability problem in Boolean logic (shortly, SAT problem), and any SAT problem can be represented by a resolvable network. Because of that, the resolution operation is valid also for resolvable networks. We can use resolution to find out or refine the inner structure of subnetworks. We give also a pessimistic and an optimistic interpretation of subnetworks. In the pessimistic case, we assume that inside a subnetwork, all communication possibilities are represented as part of the resolvable network. In the optimistic case, we assume that each subnetwork is strongly connected. We show that any SAT problem can be visualized using the pessimistic interpretation. We show that transitivity is very limited in the pessimistic interpretation, and in this case, transitivity corresponds to resolution of clauses. In the optimistic interpretation of subnetworks, we have transitivity without any further condition, but not all SAT problems can be represented in this case; however, any such network can be represented as a SAT problem. The newly introduced graphical concept allows to use terminology and tools from directed graphs in the field of SAT and also to give graphical representations of various concepts of satisfiability problems. A resolvable network is also a suitable data structure to study, for example, wireless sensor networks. The visualization power of resolvable networks is demonstrated on some pigeon hole SAT problems. Another important application field could be modeling the communication network of an information bank. Here, a subnetwork represents a dataset of a user which is secured by a proxy. Any communication should be done through the proxy, and this constraint can be checked using our model.

RCL: An A. I. Tool for Computing Maximal Consensuses

2016 ◽  
Vol 25 (04) ◽  
pp. 1650026 ◽  
Author(s):  
Éric Grégoire ◽  
Jean-Marie Lagniez
Keyword(s):  
Artificial Intelligence ◽  
Point Of View ◽  
Boolean Logic ◽  
Computational Point ◽  
Sat Problem ◽  
Single Instance ◽  
Preference Criteria ◽  
Max Sat ◽  
Internal Transformation

RCL is an original Artificial Intelligence tool for computing maximal consensuses among conflicting agents in the Boolean logic framework. It extracts one maximal set of information that does not conflict with any of the agents, taking all possible deductions into account. This form of consensus can go far beyond what is actually shared by all agents. It might be endorsed by every agent since it does not conflict with any of them. Several types of preference criteria can be selected and iterated in order to orient the computation towards some preferred consensuses. From a computational point of view RCL relies on an internal transformation of the maximal consensus-finding problem into one single instance of the Weighted Partial Max-SAT problem.

APPLICATION OF MIXED INTEGER LINEAR PROGRAMMING IN THE GENERATION OF VECTORS WITH MAXIMUM DATAPATH COVERAGE FOR COMBINATIONAL LOGIC CIRCUITS

2010 ◽  
Vol 19 (07) ◽  
pp. 1497-1516
Author(s):  
JAVIER SOSA ◽  
JUAN A. MONTIEL-NELSON ◽  
JOSE C. GARCIA-MONTESDEOCA ◽  
SAEID NOOSHABADI
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Search Algorithm ◽  
Exhaustive Search ◽  
Boolean Logic ◽  
Mixed Integer ◽  
Large Set ◽  
Combinational Logic ◽  
Sat Problem

In this paper, we present a novel methodology for vector generation that maximizes the metric of datapath coverage for a given combinational logic circuit. The proposed methodology is based on Mixed Integer Linear Programming (MILP). The search of input vectors based on the datapath coverage metric is a satisfiability (SAT) problem. In order to obtain maximum coverage vectors, we use a novel model for the Boolean logic gates to translate the original SAT problem into an MILP optimization problem. Next, the new problem is solved following the MILP optimization environment and an exhaustive search strategy. We compare our proposed methodology with the exhaustive search algorithm. Experimental results and performance comparisons based on the large set of MCNC'91 suite of benchmark circuits are presented. They show significant speedups of MILP methodology against the exhaustive search algorithm for the complex circuits.

scholarly journals Pediatric Residents and Interns in an Italian Hospital Perform Improved Bibliographic Searches when Assisted by a Biomedical Librarian

2013 ◽  
Vol 8 (1) ◽  
pp. 76
Author(s):  
Mathew Stone
Keyword(s):  
Teaching Hospital ◽  
Assessment Tool ◽  
Controlled Trial ◽  
Intervention Group ◽  
Real Life ◽  
Boolean Logic ◽  
Bibliographic Databases ◽  
Control Group ◽  
Pediatric Residents ◽  
Clinical Scenarios

A Review of: Gardois, P., Calabrese, R., Colombi, N., Lingua, C., Longo, F., Villanacci, M., Miniero, R., & Piga, A. (2011). Effectiveness of bibliographic searches performed by paediatric residents and interns assisted by librarian. A randomised controlled trial. Health Information and Libraries Journal, 28(4), 273-284. doi: 10.1111/j.1471-1842.2011.00957.x Objective – To establish whether the assistance of an experienced biomedical librarian delivers an improvement in the searching of bibliographic databases as performed by medical residents and interns. Design – Randomized controlled trial. Setting – The pediatrics department of a large Italian teaching hospital. Subjects – 18 pediatric residents and interns. Methods – 23 residents and interns from the pediatrics department of a large Italian teaching hospital were invited to participate in this study, of which 18 agreed. Subjects were then randomized into two groups and asked to spend between 30 and 90 minutes searching bibliographic databases for evidence to answer a real-life clinical question which was randomly allocated to them. Each member of the intervention group was provided with an experienced biomedical librarian to provide assistance throughout the search session. The control group received no assistance. The outcome of the search was then measured using an assessment tool adapted for the purpose of this study from the Fresno test of competence in evidence based medicine. This adapted assessment tool rated the “global success” of the search and included criteria such as appropriate question formulation, number of PICO terms translated into search terms, use of Boolean logic, use of subject headings, use of filters, use of limits, and the percentage of citations retrieved that matched a gold standard set of citations found in a prior search by two librarians (who were not involved in assisting the subjects) together with an expert clinician. Main Results – The intervention group scored a median average of 73.6 points out of a possible 100, compared with the control group which scored 50.4. The difference of 23.2 points in favour of the librarian assisted group was a statistically significant result (p value = 0.013) with a 95% confidence interval of between 4.8 and 33.2. Conclusion – This study presents credible evidence that assistance provided by an experienced biomedical librarian improves the quality of the bibliographic database searches performed by residents and interns using real-life clinical scenarios.

A polynomial algorithm of edge-neighbor-scattering number of trees

2016 ◽  
Vol 283 ◽  
pp. 1-5 ◽  
Author(s):  
Yong Liu ◽  
Zongtian Wei ◽  
Jiarong Shi ◽  
Anchan Mai
Keyword(s):  
Polynomial Algorithm

scholarly journals Digital logic gates in soft, conductive mechanical metamaterials

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Charles El Helou ◽  
Philip R. Buskohl ◽  
Christopher E. Tabor ◽  
Ryan L. Harne
Keyword(s):  
Integrated Circuits ◽  
Electronic Materials ◽  
Polymer Networks ◽  
Conductive Polymer ◽  
Network Connectivity ◽  
Logic Gates ◽  
Boolean Logic ◽  
Digital Logic ◽  
Mechanical Metamaterials ◽  
Logic Operations

AbstractIntegrated circuits utilize networked logic gates to compute Boolean logic operations that are the foundation of modern computation and electronics. With the emergence of flexible electronic materials and devices, an opportunity exists to formulate digital logic from compliant, conductive materials. Here, we introduce a general method of leveraging cellular, mechanical metamaterials composed of conductive polymers to realize all digital logic gates and gate assemblies. We establish a method for applying conductive polymer networks to metamaterial constituents and correlate mechanical buckling modes with network connectivity. With this foundation, each of the conventional logic gates is realized in an equivalent mechanical metamaterial, leading to soft, conductive matter that thinks about applied mechanical stress. These findings may advance the growing fields of soft robotics and smart mechanical matter, and may be leveraged across length scales and physics.

Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem

2021 ◽  
Vol 31 (1) ◽  
pp. 1-4
Author(s):  
Mikhail A. Cherepnev
Keyword(s):  
Upper Bound ◽  
Polynomial Algorithm ◽  
Integer Factorization ◽  
Factorization Problem ◽  
Diffie Hellman ◽  
Integer Factorization Problem

Abstract We construct a probabilistic polynomial algorithm that solves the integer factorization problem using an oracle solving the Diffie–Hellman problem.

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