Extension Rule Based Model Counting Using More Reasoning

2010 ◽  
Vol 108-111 ◽  
pp. 268-273 ◽  
Author(s):  
Jun Ping Zhou ◽  
Chun Guang Zhou ◽  
Ming Hao Yin ◽  
Hui Yang
Keyword(s):  
New Method ◽  
Propositional Formula ◽  
Rule Based ◽  
Extension Rule ◽  
Model Counting

Extension rule is a new method for computing the number of models for a given propositional formula. In some sense, it is actually an inverse propositonal resolution. In order to improve counting performance, we introduce some reasoning rules into extension rule based model counting and present a new algorithm RCER which combines the extension rule and the reasoning rule together. The experiment results show that the algorithm not only occupies less space but also increases the efficiency for solving model counting.

scholarly journals A Parallel Extension Rule-Based Algorithm for #SAT Problem Using Model-Counting Tree

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 41042-41049
Author(s):  
Naiyu Tian ◽  
Dantong Ouyang ◽  
Fengyu Jia ◽  
Meng Liu ◽  
Liming Zhang
Keyword(s):  
Rule Based ◽  
Sat Problem ◽  
Extension Rule ◽  
Model Counting ◽  
Parallel Extension

Chapter 25. Model Counting

2021 ◽  
Author(s):  
Carla P. Gomes ◽  
Ashish Sabharwal ◽  
Bart Selman
Keyword(s):  
Local Search ◽  
Upper Bound ◽  
Probabilistic Inference ◽  
Efficient Algorithms ◽  
Propositional Formula ◽  
Exact Methods ◽  
Complete Problem ◽  
Model Counting ◽  
New Ideas

Model counting, or counting the number of solutions of a propositional formula, generalizes SAT and is the canonical #P-complete problem. Surprisingly, model counting is hard even for some polynomial-time solvable cases like 2-SAT and Horn-SAT. Efficient algorithms for this problem will have a significant impact on many application areas that are inherently beyond SAT, such as bounded-length adversarial and contingency planning, and, perhaps most importantly, general probabilistic inference. Model counting can be solved, in principle and to an extent in practice, by extending the two most successful frameworks for SAT algorithms, namely, DPLL and local search. However, scalability and accuracy pose a substantial challenge. As a result, several new ideas have been introduced in the last few years that go beyond the techniques usually employed in most SAT solvers. These include division into components, caching, compilation into normal forms, exploitation of solution sampling methods, and certain randomized streamlining techniques using special constraints. This chapter discusses these techniques, exploring both exact methods as well as fast estimation approaches, including those that provide probabilistic or statistical guarantees on the quality of the reported lower or upper bound on the model count.

Granular Synthesis of Rule-Based Models and Function Approximation Using Rough Sets

2010 ◽  
pp. 408-425 ◽  
Author(s):  
Carlos Pinheiro ◽  
Fernando Gomide ◽  
Otávio Carpinteiro ◽  
Isaías Lima
Keyword(s):  
Nonlinear Systems ◽  
Rough Sets ◽  
Estimation Procedure ◽  
New Method ◽  
Rule Based ◽  
Numerical Examples ◽  
Rule Sets ◽  
Computational Procedures ◽  
Granular Synthesis ◽  
And Function

This chapter suggests a new method to develop rule-based models using concepts about rough sets. The rules encapsulate relations among variables and give a mechanism to link granular descriptions of the models with their computational procedures. An estimation procedure is suggested to compute values from granular representations encoded by rule sets. The method is useful to develop granular models of static and dynamic nonlinear systems and processes. Numerical examples illustrate the main features and the usefulness of the method.

Solving #QBF Using Extension Rule

2010 ◽  
Vol 26-28 ◽  
pp. 250-254
Author(s):  
Jun Ping Zhou ◽  
Chun Guang Zhou ◽  
Yan Dong Zhai ◽  
Yong Juan Yang
Keyword(s):  
Component Analysis ◽  
New Method ◽  
Quantified Boolean Formulas ◽  
Extension Rule ◽  
Boolean Formulas ◽  
Unit Propagation

Extension rule is a new method for computing the number of models for SAT formulae. In this paper, we investigate the use of the extension rule in solving #QBF, i.e., computing the number of Q1x1…Qn xn which makes the Quantified Boolean Formulas (QBF) Q1x1…Qn xnF evaluate to true. We present a #QBF algorithm based on the extension rule, namely QBFMC, which also integrates the unit propagation and the component analysis together. These excellent technologies improve the efficiency of solving #QBF problems efficiently.

scholarly journals A Recursive Algorithm for Projected Model Counting

2019 ◽  
Vol 33 ◽  
pp. 1536-1543 ◽  
Author(s):  
Jean-Marie Lagniez ◽  
Pierre Marquis
Keyword(s):  
Standard Model ◽  
Recursive Algorithm ◽  
Propositional Formula ◽  
Decomposition Scheme ◽  
Model Counting

We present a recursive algorithm for projected model counting, i.e., the problem consisting in determining the number of models k∃X.Σk of a propositional formula Σ after eliminating from it a given set X of variables. Based on a ”standard” model counter, our algorithm projMC takes advantage of a disjunctive decomposition scheme of ∃X.Σ for computing k∃X.Σk. It also looks for disjoint components in its input for improving the computation. Our experiments show that in many cases projMC is significantly more efficient than the previous algorithms for projected model counting from the literature.

scholarly journals Using Fuzzy Logic in Robot Navigation to Find Animals

2014 ◽  
Vol 12 (4) ◽  
pp. 3382-3392 ◽  
Author(s):  
Mahdi Amiri ◽  
Zeinab Abbasi ◽  
Fakhte Soltani Tafreshi
Keyword(s):  
Fuzzy Logic ◽  
Endangered Species ◽  
Autonomous Robots ◽  
Robot Navigation ◽  
Fuzzy Rule ◽  
Fuzzy Rules ◽  
New Method ◽  
Matlab Software ◽  
Rule Based ◽  
Rule Based Systems

 Fuzzy logic is a tool to use human expertise. The simplicity of fuzzy-rule based systems and its power to perform various tasks without accurate measurement and computation makes it very popular between sciences. One of these applications is using fuzzy logic in designing the controller for navigation of autonomous robots to move in various environments. This paper proposes a new method of robot navigation based on fuzzy logic. This method can be drawn upon to design robots which can find and catch different kind of animals, especially endangered species. It works based on a hierarchical set of behavior each of which acts by using a set of fuzzy rules. The proposed method is simulated and tested by MATLAB software.

scholarly journals A New Method to Compare the Interpretability of Rule-Based Algorithms

AI ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 621-635
Author(s):  
Vincent Margot ◽  
George Luta
Keyword(s):  
Predictive Model ◽  
Simple Formula ◽  
Model Analysis ◽  
New Method ◽  
Weighted Sum ◽  
Rule Based ◽  
Predictive Algorithms ◽  
Rule Sets ◽  
Definition Of ◽  
Sørensen Index

Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this paper is to propose the definition of a score that allows for quickly comparing interpretable algorithms. This definition consists of three terms, each one being quantitatively measured with a simple formula: predictivity, stability and simplicity. While predictivity has been extensively studied to measure the accuracy of predictive algorithms, stability is based on the Dice-Sorensen index for comparing two rule sets generated by an algorithm using two independent samples. The simplicity is based on the sum of the lengths of the rules derived from the predictive model. The proposed score is a weighted sum of the three terms mentioned above. We use this score to compare the interpretability of a set of rule-based algorithms and tree-based algorithms for the regression case and for the classification case.

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