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Half tensor product SAT solving method and device based on conjunctive normal form

A conjunctive paradigm and semi-tensor product technology, applied in the computer field, can solve problems such as inapplicability to solving large-scale SAT problems, inability to guarantee problem satisfiability, difficulty of SAT solvers, etc., to optimize calculation accuracy and improve The effect of compactness and calculation time improvement

Pending Publication Date: 2022-07-08
上海华大九天信息科技有限公司
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  • Abstract
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  • Claims
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Problems solved by technology

Like most computing tools, traditional SAT solvers are implemented by software, and their solving algorithms are divided into complete algorithms and incomplete algorithms. The complete algorithm exhaustively searches the solution space of the SAT formula, and in theory, a certain SAT solver can be obtained. The conclusion of the satisfaction of the formula, but the SAT problem is an NP problem, and its solution space grows exponentially with the number of variables in the formula, so this algorithm is inefficient and not suitable for solving large-scale SAT problems
In addition, the incomplete algorithm does not search the entire solution space, but uses a heuristic method to search part of the solution space. The solution speed is faster, but it does not guarantee that the satisfiability of the SAT problem can be judged.
[0004] The number of variables contained in the CNF formula of the current practical system has increased sharply, and the correlation of variables in practical problems has become stronger and stronger. SAT solvers have found it difficult to cope with the above challenges

Method used

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  • Half tensor product SAT solving method and device based on conjunctive normal form
  • Half tensor product SAT solving method and device based on conjunctive normal form
  • Half tensor product SAT solving method and device based on conjunctive normal form

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Embodiment 1

[0061] figure 1 It is a schematic diagram of the semi-tensor product SAT solving device based on conjunctive normal form according to the present invention, such as figure 1 As shown, the semi-tensor product SAT solving device based on conjunctive normal form of the present invention includes a clause parsing module 10, a matrix conversion module 20, an assignment solving module 30 and a satisfiable decombining module 40, wherein,

[0062] The clause parsing module 10 is used to segment the input conjunctive normal form, ie, the CNF formula, and parse it into the form to be solved.

[0063] The matrix conversion module 20 is configured to convert the to-be-solved form parsed by the clause parsing module 10 into a corresponding to-be-solved matrix form.

[0064] The assignment and solving module 30 is used for assigning a value to the matrix to be solved, and the assignment case sentence of each clause is independent of other clauses.

[0065] The satisfiable solution merging...

Embodiment 2

[0067] figure 2 For the flow chart of the semi-tensor product SAT solution method based on conjunctive normal form according to the present invention, the following will refer to figure 2 , and describe in detail the semi-tensor product SAT solution method based on conjunctive normal form of the present invention.

[0068] First, in step 101, the conjunctive normal form clause is parsed.

[0069] Preferably, the CNF formula is parsed by a parser, and two integer variables are defined: V and C, where V represents the number of variables in the formula; C represents the number of independent clauses in the formula. Define C independent disjunctive clauses: C x , where C x The Boolean relationship between the variables in is "or", and the value range of x is 0

[0070] In step 102, according to the conjunctive normal form clauses obtained by parsing, each clause C is x The representation is converted into the corresponding logical matrix representation M x , and will...

Embodiment 3

[0091] image 3 It is a schematic diagram of an example of a matrix-half-tensor product product according to an embodiment of the present invention. like image 3 As shown, by dividing and matching the dimensions of the front and rear matrices, the calculation of the multiplication of two matrices with different dimensions is realized.

[0092] Figure 4 It is a schematic diagram of the solution flow of the traditional SAT solver based on the conjunction normal form according to the first embodiment of the present invention. like Figure 4 As shown, first randomly select a variable a or b or c for assignment, and at the same time form the data structure of the binary tree, and then because the constraint of SAT is that the expression can be satisfied, that is, equal to 1, then assign the next variable until all variables are Assignment ends. If the result of SAT is obtained, it will be returned. If the result of UNSAT is obtained, it goes back to the previous assignment ...

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Abstract

A semi-tensor product SAT solving method based on a conjunctive normal form comprises the steps that a conjunctive normal form clause is analyzed; according to the combined normal form clauses obtained through analysis, converting each clause Cx representation into a corresponding logic matrix representation Mx, and combining the obtained Mx into a group of matrix expressions through a logic relationship; solving and calculating a logic matrix representation according to a semi-tensor product SAT; and according to the satisfactory assignment of each Cx, obtaining an intersection of each group of satisfactory assignments to obtain a group of satisfactory Boolean assignments satisfying all the independent clauses C. According to the semi-tensor product SAT solving method and device based on the conjunctive normal form, the calculation time can be shortened, the calculation efficiency can be improved, and the compactness of the satisfactory solution can be improved.

Description

technical field [0001] The invention relates to the field of computer technology, in particular to a method and device for solving a semi-tensor product SAT based on conjunctive normal form. Background technique [0002] The Boolean satisfiability problem (ie, SAT problem) is the first NP problem to be proved (ie, a non-deterministic problem that can be solved by polynomial algorithms), and the method to solve this problem is in EDA (electronic design automation, that is, electronic design automation). It plays an important role, such as combinatorial equivalence checking, formal verification, model checking, logical reasoning, integrated circuit design, etc. [0003] In theory, the SAT problem is used to determine whether a Boolean logic formula has a set of satisfiable solutions, that is, a set of assignments to Boolean variables that make the Boolean formula true. Therefore, the actual problem needs to be converted into a Boolean formula before it can be solved using the...

Claims

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Application Information

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IPC IPC(8): G06F30/327G06F17/16
CPCG06F30/327G06F17/16
Inventor 储著飞潘鸿洋雍晓董森华
Owner 上海华大九天信息科技有限公司
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