Algebraic-based fast logic decision-making method

A decision-making method and fast technology, applied in the computer field, can solve problems such as difficult to solve scale, optimization problems are not convex, and cannot give effective results, etc., to achieve the effect of improving efficiency and saving energy

Inactive Publication Date: 2018-04-20
CHONGQING INST OF GREEN & INTELLIGENT TECH CHINESE ACADEMY OF SCI +1
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Problems solved by technology

Theoretically speaking, a complete DPLL method can always determine whether a given Boolean propositional logic formula can be satisfied; but its worst computational complexity is exponential, which makes it difficult to solve large-scale complex problems
Local DPLL methods may have advantages in solving large-scale satisfiable formulas, but if the formula itself is unsa

Method used

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  • Algebraic-based fast logic decision-making method
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  • Algebraic-based fast logic decision-making method

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Embodiment

[0049] Example: In electronic automation design, circuit loops are often described by an equivalent Boolean propositional logic formula. Then look at the compatibility of the circuit by checking the satisfiability of Boolean propositional logic formulas.

[0050] In this example, suppose we get a Boolean propositional logic formula

[0051]

[0052] If we need to determine whether the formula (1) is a 1-in-3 satisfiable formula, we need to convert the formula into a formula containing only positive text

[0053] (X 1 ∨X 2 ∨X 3 )∧(Y 1 ∨X 2 ∨X 3 )∧(X 1 ∨Y 1 ) (2)

[0054] Then, according to the formula Transform formula (2) into a linear Boolean system

[0055]

[0056] Step 6: Carry out secondary continuation of formula (3). Other U=(X 1 ,X 2 ,X 3 ,Y 1 ) T , is 1 where all elements are unit one 4×4 order square matrix, then the quadratic continuation Boolean equations are

[0057]

[0058] Step seven, perform linear abstraction on formula (4). ...

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Abstract

The invention relates to an algebraic-based fast logic decision-making method, and belongs to the field of computers. According to the method, the inner nature and secondary invariant properties of the boolean value are fully utilized, and an abstract extraction technology is adopted to turn the satisfaction problem of a boolean propositional logic into a problem for solving a linear equation set,so that the non-satisfaction logic decision problem can be rapidly judged under the complex degree of the polynomial time. Meanwhile, the core technical support is provided for fast judging whether the logic decision-making problem can be met. The method can be applied to artificial intelligence, robots, automatic reasoning, logic planning, graph matching, network structure comparison, computer-aided manufacturing, computer graphics, computer system structure design, electronic design automation, database system and the scheduling optimization and the like can be realized, the efficiency canbe improved, and the energy can be saved.

Description

technical field [0001] The invention belongs to the field of computers and relates to an algebra-based fast logic decision-making method. Background technique [0002] In computer science and engineering, many calculation and decision problems can be efficiently reduced to the satisfiability judgment problem of Boolean propositional logic formulas. Therefore, if the satisfiability judgment of the Boolean propositional logic formula can be quickly performed, the related computer decision-making problems can be solved efficiently. However, the problem of judging the satisfiability of Boolean propositional logic formulas has been proved to be an NP-complete problem in theory. So far, there is no polynomial time complexity algorithm for such problems that can determine the satisfiability of Boolean propositional logic formulas. [0003] The satisfiability determination methods of traditional Boolean propositional logic formulas are divided into two categories. A large class o...

Claims

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Application Information

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IPC IPC(8): G06T17/10
CPCG06T17/10
Inventor 刘江方成玲
Owner CHONGQING INST OF GREEN & INTELLIGENT TECH CHINESE ACADEMY OF SCI
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