Boolean satisfiability judgment method based on linear programming

A Boolean satisfiability and linear programming technology, applied in the field of logic circuits, can solve problems such as difficult to solve scale, optimization problems are not convex, and unreliable results, and achieve the effects of improving efficiency, saving energy, and quickly determining

Pending Publication Date: 2022-02-25
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 is satisfiable; 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 unsatisfiable and has a large minimum unsatisfiable kernel, this method usually cannot give effective results
The optimization-based method once had obvious advantages in efficiency, but because the corresponding optimization problem is not convex, it is likely to obtain a local optimum
The results in this case are unreliable, and this type of method has gradually fallen silent

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  • Boolean satisfiability judgment method based on linear programming
  • Boolean satisfiability judgment method based on linear programming
  • Boolean satisfiability judgment method based on linear programming

Examples

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Embodiment

[0047] Example: In electronic automatic design, a circuit loop is often described by an equivalent Boolean propositional logic formula, and then the logic circuit is checked by checking the satisfiability of the Boolean propositional logic formula.

[0048] In this example, assuming that the satisfiability of a logic circuit needs to be judged, we propose a "Boolean satisfiability judgment method based on linear programming".

[0049] Preferred examples of the present invention will be described in detail below with reference to the accompanying drawings.

[0050] like figure 1 Shown, the steps of the present invention are as follows:

[0051] S1: combine figure 2 , analyze the satisfiability of the logic circuit, and extract the Boolean propositional logic formula as:

[0052] Described Boolean propositional logic formula is by 4 Boolean variables X=(X 1 , X 2 , X 3 , X 4 ), operators AND (connection, represented by ^), OR (separation, represented by express), N...

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Abstract

The invention relates to a Boolean satisfiability judgment method based on linear programming, which belongs to the field of logic circuits, and comprises the following steps: S1, extracting a Boolean proposition logic formula; S2, converting into a CNF Boolean logic formula which can be satisfied; S3, converting the problem into a 3-SAT problem in a CNF form; S4, converting the problem into a 1-in-3-SAT problem; S5, equivalently converting into an optimal value problem of linear programming; S6, solving precision setting is carried out on an optimal value solving problem of linear programming; S7, solving the optimal value of the linear programming problem, and judging the satisfiability of the Boolean proposition logic formula according to the optimal value; and S8, for the satisfactory Boolean proposition logic formula, recursively adding constraints to the linear programming problem and solving the linear programming problem to obtain an answer of the satisfactory problem. Rapid judgment under the polynomial time complexity is realized, the judgment efficiency can be improved, and energy is saved.

Description

technical field [0001] The invention relates to a Boolean satisfiability judgment method based on linear programming, which belongs to the field of logic circuits, in particular to a Boolean satisfiability judgment based on linear programming. Background technique [0002] In computer science and engineering, the problem of determining whether a given problem has a solution is often encountered, usually requiring an answer to the problem when there is a solution. Such problems can be efficiently (polynomial time) reduced to the problem of judging the satisfiability of Boolean propositional logic formulas. Therefore, if the satisfiability judgment of the Boolean propositional logic formula can be quickly carried out, the relevant 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 comp...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/3323
CPCG06F30/3323
Inventor 刘江方成玲
Owner CHONGQING INST OF GREEN & INTELLIGENT TECH CHINESE ACADEMY OF SCI
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