SAT problem processing system and processing method

Abstract

The invention provides an SAT problem processing system, which utilizes a photoelectric hybrid computing device comprising an optical domain matrix device and a threshold value judging device for processing, and is characterized by comprising a problem conversion module for obtaining an adjacent matrix and an external field vector associated with a CNF normal form of an SAT problem based on the characteristics of the Isinin problem; the setting module is used for setting the optical domain matrix device and the threshold value judging device according to the adjacent matrix and the external field vector; and the algorithm module is used for determining the optimal solution of the SAT problem through the optical domain matrix device and the threshold judging device.

Description

Technical Field

[0001] The present invention relates to the field of optical computing, and in particular to a SAT problem processing system and method for solving the SAT problem by using an optoelectronic hybrid computing device. Background Art

[0002] The SAT problem, or Boolean Satisfiability Problem, is a well-known decision problem that belongs to the NP problem (Non-deterministic Polynomial Problem). It appears in many fields such as theoretical computer science and mathematics, and is closely related to many practical problems. For example, circuit design, planning, constraint satisfaction problems, etc. can all be converted into SAT problems.

[0003] The SAT problem is not only of great significance in basic research such as mathematical logic and computational complexity theory, but also has high application value in many practical production fields such as operations research, computer science, artificial intelligence, and very large-scale integrated circuit design. In particular, in the field of electronic design automation (EDA) of integrated circuits, the SAT problem can be used to verify the correctness of the design, detect design errors, and optimize the design. It plays an important role in logic synthesis, formal verification, and circuit testing. Therefore, how to accurately solve the SAT problem has become a basic core task in EDA applications.

[0004] However, since the SAT problem is an NP-hard problem, that is, it cannot be solved deterministically in polynomial time, but can be solved in non-deterministic polynomial time. This means that as the size of the problem increases, the time complexity of the solution will increase dramatically. In particular, in EDA applications, SAT problems usually involve a large number of variables and constraints, and have complex logical relationships. This further increases the size of the problem and the difficulty of solving it. In addition, there may be some unforeseen factors in many actual situations, such as hardware failures, signal interference, etc., which will also affect the solution of the SAT problem.

[0005] Therefore, studying and implementing efficient SAT problem-solving methods is an important issue that needs to be solved urgently.

[0006] At present, the algorithms for solving SAT problems mainly include two categories: deterministic algorithms and random search algorithms.

[0007] Deterministic algorithms are a method based on reasoning and proof, which solves SAT problems through deduction and logical reasoning. The time required for solving deterministic algorithms increases exponentially with the growth of the problem size, and is not suitable for solving large-scale SAT problems.

[0008] The random search algorithm is mainly based on the local search idea and uses a heuristic strategy to guide the search for a solution to the SAT problem. It can get a solution faster than the deterministic algorithm when dealing with large-scale satisfiable SAT problems. However, as the scale and complexity of the problem increase, the random search algorithm faces the problem of slow convergence, easy to fall into the local optimal solution, and unable to find the global optimal solution.

[0009] In addition, in addition to the problems with the algorithm, in terms of hardware, since the CPU / GPU is subject to architectural and process limitations, the performance is increasingly approaching the limit, and the room for improving computing power has encountered a bottleneck, making it difficult to achieve efficient SAT problem solving.

[0010] In recent years, optical computing methods that use optical systems to simulate Ising spin systems to solve NP problems have been greatly developed, including spatial light modulation Ising machines, coherent Ising machines, and photonic neural network Ising machines based on cascaded Mach-Zehnder interferometers (MZIs). These optical computing methods fully utilize the advantages of light parallelism, low latency, and low energy consumption, and have achieved performance that exceeds that of classical computers running specific heuristic algorithms in solving the maximum cut problem, a type of NP problem. However, for other NP problems, including the SAT problem, there is still a lack of corresponding scientific research on whether this optical computing method can be used to solve or even accelerate the solution.

[0011] In view of this, in order to solve the above problems, the purpose of the present invention is to provide a SAT problem processing system and processing method, which can utilize an optoelectronic hybrid computing device to solve the SAT problem efficiently and quickly. At the same time, it can not only solve the problem that the solution time in the deterministic algorithm increases exponentially with the growth of the problem scale, but also solve the problem that the random search algorithm has slow convergence speed and is easy to fall into the local optimal solution and thus cannot find the global optimal solution. Summary of the invention

[0012] The first aspect of the present invention relates to a SAT problem processing system, which uses an optoelectronic hybrid computing device including an optical domain matrix device and a threshold value judgement device for processing, and is characterized in that it includes:

[0013] A problem conversion module, which obtains an adjacency matrix and an external field vector associated with a CNF paradigm of the SAT problem based on the characteristics of the Ising problem;

[0014] A setting module, which sets the light domain matrix device and the threshold value determiner according to the adjacency matrix and the external field vector; and

[0015] An algorithm module is used to determine the optimal solution of the SAT problem through the light domain matrix and the threshold value determiner.

[0016] The second aspect of the present invention is that in the first aspect, the problem conversion module simplifies the CNF paradigm of the SAT problem, constructs the QUBO problem using the simplified CNF paradigm, and then converts the QUBO problem into the Hamiltonian function form of the Ising problem, thereby deriving the adjacency matrix and the external field vector.

[0017] The third aspect of the present invention is that, in the second aspect, the problem conversion module implements the simplification by preprocessing the CNF paradigm, wherein the preprocessing includes converting a polynomial clause having a number of literal variables greater than 3 into a ternary clause.

[0018] The fourth aspect of the present invention is that in any one of the first to third aspects, the setting module sets the threshold judgement device corresponding to each component of the output vector of the optical domain matrix device based on the adjacency matrix and the external field vector.

[0019] A fifth aspect of the present invention resides in that, in the first aspect, the threshold value determiner is a nonlinear threshold value determiner.

[0020] The sixth aspect of the present invention is that in the first aspect, the algorithm module uses a Gaussian noise vector to set an iterative mathematical formula, and recursively solves the iterative mathematical formula to determine the optimal solution.

[0021] The seventh aspect of the present invention is that, in the sixth aspect, the iterative mathematical formula is used to iterate the text variables of the SAT problem, and the optimal energy and the optimal text variables are determined according to the energy obtained in each iteration until a preset maximum number of iterations is reached.

[0022] An eighth aspect of the present invention relates to a method for processing a SAT problem, which is processed by using an optoelectronic hybrid computing device including an optical domain matrix device and a threshold value judgement device, and is characterized in that it includes:

[0023] A problem transformation step, in which, based on the characteristics of the Ising problem, an adjacency matrix and an external field vector associated with the CNF normal form of the SAT problem are obtained;

[0024] A setting step, in which the light domain matrix device and the threshold value determiner are set according to the adjacency matrix and the external field vector; and

[0025] Algorithm step, in which the optimal solution of the SAT problem is determined by the light domain matrix device and the threshold value determiner.

[0026] The ninth aspect of the present invention is that in the eighth aspect, in the problem conversion step, the CNF paradigm of the SAT problem is simplified by preprocessing the CNF paradigm, and the preprocessing includes converting a polynomial clause with a number of literal variables greater than 3 into a ternary clause.

[0027] The tenth aspect of the present invention is that in the eighth aspect or the ninth aspect, in the setting step, the threshold judgement device corresponding to each component of the output vector of the optical domain matrix device is set based on the adjacency matrix and the external field vector.

[0028] The eleventh aspect of the present invention is that in the eighth aspect, in the algorithm step, a Gaussian noise vector is used to set an iterative mathematical formula, and a recursive solution is performed through the iterative mathematical formula to determine the optimal solution.

[0029] According to the SAT problem processing system and processing method involved in the present invention, the SAT problem can be solved efficiently and quickly using an optoelectronic hybrid computing device. At the same time, it can not only solve the problem that the solution time in the deterministic algorithm increases exponentially with the growth of the problem scale, but also solve the problem that the random search algorithm has a slow convergence speed and is easy to fall into the local optimal solution and thus cannot find the global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a block diagram of the SAT problem processing system involved in the first embodiment of the present invention.

[0031] Figure 2 This is a functional block diagram for realizing a matrix multiplication function in the optical domain according to the first embodiment of the present invention.

[0032] Figure 3 It is a schematic diagram of the structure of an optoelectronic hybrid computing device for solving the SAT problem according to the first embodiment of the present invention.

[0033] Figure 4 This is a flowchart of a recursive algorithm for solving the Ising problem according to the first embodiment of the present invention.

[0034] Figure 5 It is a flowchart of the SAT problem processing method involved in embodiment 2 of the present invention. DETAILED DESCRIPTION

[0035] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings, so that ordinary technicians in this field will be more aware of the features, objects and advantages of the present invention.

[0036] In the following content, many specific details are described to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from these, and the present invention is not limited to the specific implementation modes disclosed below.

[0037] Implementation Method 1

[0038] Embodiment 1 relates to a SAT problem processing system, Figure 1 A block diagram showing a SAT problem processing system 100 according to the first embodiment of the present invention.

[0039] The SAT problem processing system 100 is a system for solving SAT problems using an optoelectronic hybrid computing device. Figure 1 As shown, the SAT problem processing system 100 involved in Embodiment 1 includes a problem conversion module 110 , a setting module 120 and an algorithm module 130 .

[0040] The following is a detailed description of the structure and function of each module.

[0041] <Question conversion module 110>

[0042] The problem conversion module 110 in the SAT problem processing system 100 first simplifies the CNF normal form (Conjunctive Normal Form, referred to as CNF) of the SAT problem to be solved, constructs the QUBO problem (Quadratic Unconstrained Binary Optimization) using the simplified CNF normal form, and then converts the QUBO problem into the Hamiltonian function form of the Ising problem, thereby deriving the adjacency matrix and external field vector of the Ising problem. In other words, the problem conversion module 110 obtains the adjacency matrix and external field vector associated with the above CNF normal form of the SAT problem based on the characteristics of the Ising problem.

[0043] Specifically, the problem conversion module 110 includes a preprocessing unit 111 , a QUBO problem construction unit 112 and an objective function conversion unit 113 .

[0044] The problem conversion module 110 preprocesses the SAT problem to be solved through the preprocessing unit 111, thereby simplifying the CNF paradigm of the SAT problem. The preprocessing performed by the preprocessing unit 111 is described in detail below.

[0045] Suppose there is an arbitrary SAT problem to be solved, and the Boolean expression of the SAT problem is expressed in the form of conjunctive normal form (hereinafter referred to as CNF). Conjunctive normal form is a classic formal method for expressing Boolean expressions. It consists of multiple clauses connected by conjunctive connectives to facilitate the solution of SAT problems.

[0046] As we all know, in the CNF paradigm of SAT problems, a clause is a disjunction consisting of several literals. Literals (hereinafter sometimes referred to as variables or literal variables) are one of the basic elements that make up a clause. Each clause consists of several literals, which are connected by disjunctive conjunctions. Literals can be variables themselves or the negation of variables, such as x or non-x. A unit clause is a clause that contains only one variable or its negation.

[0047] In the SAT problem processing system 100 according to the first embodiment, the preprocessing unit 111 eliminates unique solution variables in the CNF normal form of the SAT problem based on unit clauses in the CNF normal form.

[0048] Specifically, for any SAT problem to be solved, assuming that C i is the i-th clause in its CNF form, and C i is a unit clause, then C i =x j or Among them, x j represents the jth word, Indicates the jth character x j negation.

[0049] Obviously, x in the unit clause j The solution is unique. That is, only x j =1 or x j = 0 to make C i = 1. Get x j After finding the only solution of j Substitute the value into all the j If the clause is 1, eliminate the corresponding clause. If it is not certain whether the clause is satisfied, eliminate x in the clause. j The preprocessing unit 111 eliminates the unique solution variable in the CNF paradigm in this way, thereby reducing the number of variables in the CNF paradigm and further reducing the scale of the SAT problem to be solved.

[0050] Furthermore, for the CNF paradigm after eliminating the unique solution variable, the preprocessing unit 111 converts the polynomial clause with more than 3 characters into a ternary clause. If there are binary or ternary clauses in the CNF paradigm, the original binary or ternary clauses are retained. Through this processing, the introduction of auxiliary variables when constructing the QUBO problem described later can be minimized, thereby further avoiding the expansion of the scale of the SAT problem. In addition, as to how to convert a polynomial clause with more than 3 character variables into a ternary clause, methods known in the art can be used.

[0051] At this point, the preprocessing unit 111 obtains a CNF paradigm with binary or ternary clauses through the above preprocessing, and outputs the CNF paradigm to the QUBO problem construction unit 112.

[0052] Next, in the QUBO problem construction unit 112, a QUBO problem is constructed using the CNF paradigm with binary or ternary clauses obtained from the preprocessing unit 111. The QUBO problem is an integer programming problem, which can be used to represent various combinatorial optimization problems. Since the objective function of the QUBO problem is a quadratic function of binary variables, by converting the CNF paradigm into a QUBO problem, it can be solved using existing quantum computers and optimization algorithms. How to construct a QUBO problem is common knowledge in the field, and can be constructed using conversion methods commonly used in the field. In this embodiment 1, the following case is taken as an example for illustration.

[0053] First, for each clause C in the CNF paradigm processed by the preprocessing unit 111, i Construct a clause objective function φ(C i ). The total objective function of the entire CNF paradigm is the maximum sum of the objective functions of all clauses, that is:

[0054]

Mathematical formula 1

[0055] F=maxΣ Ci φ(C i ).

[0056] Then, rewrite it as the objective function of the QUBO problem to obtain:

[0057]

Mathematical formula 2

[0058] F=-H,

[0059] H=min x T Q x ,

[0060] Among them, x represents a text vector, x=(x 1 ,x 2 ,···,xn ), contains a total of n text variables, Q is the Q matrix of the QUBO problem, with dimension n×n.

[0061] The QUBO problem construction unit 112 outputs the obtained objective function of the QUBO problem to the objective function conversion unit 113 .

[0062] The QUBO problem is a special optimization problem, which can be converted into an Ising model problem for solution, and the Ising model has the characteristics of being easy to numerically calculate and easy to implement on a quantum computer. Therefore, the objective function conversion unit 113 receives the objective function of the QUBO problem and converts the objective function of the QUBO problem into the Hamiltonian function form of the Ising problem. How to convert the objective function of the QUBO problem into the Ising problem is common knowledge in the art, and a conversion method commonly used in the art can be used. In this embodiment 1, the following case is taken as an example for explanation.

[0063] The Ising problem is a physical model that describes spin interactions. i =2x i -1, thus rewriting H in the above [Mathematical Formula 2] into the Hamiltonian function form of the Ising problem, that is:

[0064]

Mathematical formula 3

[0065] H=min(-1 / 2Σ ij K ij σ i σ j -Σ i L i σ i +1 / 4Tr(Q)+1 / 4Σ ij Q ij ),

[0066] Where K is the adjacency matrix of the Ising problem, with dimension n×n, i, j are the subscripts of the elements of K matrix. In addition, let K = -Q / 2, and K ii = 0, L is the external field vector of the Ising problem, with a dimension of n×1, and is set to L i =-1 / 2Σ j Q ij . In which, let i = 1, 2, 3..., n, and j = 1, 2, 3... n. Tr(Q) is the trace of the Q matrix, i.e., the sum of the diagonals. The last two terms are independent of the spin variable and sum up to a constant.

[0067] Through the objective function conversion unit 113, based on the above [Mathematical Formula 3], an Ising problem in the form of a Hamiltonian function is finally obtained, and the adjacency matrix K and the external field vector L of the Ising problem are derived.

[0068] <Setting Module 120>

[0069] The setting module 120 in the SAT problem processing system 100 is used to set the optical domain matrix device and the threshold judgement device of the optoelectronic hybrid computing device according to the adjacency matrix K and the external field vector L of the Ising problem obtained by the problem conversion module 110, so as to obtain the optoelectronic hybrid computing device after the setting is completed, which is used for solving the SAT problem described later.

[0070] Figure 2 This is a functional block diagram for realizing a matrix multiplication function in the optical domain according to the first embodiment. Figure 3 It is a schematic diagram of the structure of the optoelectronic hybrid computing device for solving the SAT problem involved in the first embodiment.

[0071] First, a specific method of implementing the optical domain matrix multiplication function using the optical domain matrix device 200 according to the first embodiment will be described. Figure 2 In the example, in order to simplify the drawings and facilitate understanding, the dimension n=2 of the adjacency matrix K is used as an example for explanation, that is, the product of a 2x2 matrix and a 2x1 vector is used as an example for explanation. However, this embodiment can also be applied to the case where n>2 (n is an integer).

[0072] like Figure 2 As shown, suppose there are two light signals 1 and 2 as input, both with the intensity of I 0 . Optical signal 1(I 0 ) and optical signal 2(I 0 ) is input to the optical domain matrix device 200 via two input modulators 201 and 202. The modulation voltages of the two input modulators 201 and 202 are respectively set to V 1 、V 2 .

[0073] Then, the optical domain matrix device 200 performs optical domain matrix multiplication operation on the light intensity modulated by the two input modulators 201 and 202, and finally obtains the multiplication output of the optical domain matrix, namely output component (hereinafter also referred to as output vector) 1 and output component (hereinafter also referred to as output vector) 2.

[0074] Secondly, Figure 3 The specific structure of the optoelectronic hybrid computing device according to the first embodiment is described below. Figure 3 In the example, the adjacency matrix K ij The optical-electrical hybrid computing device according to the first embodiment mainly includes the optical domain matrix device 200 and the threshold value determination device 210 described above.

[0075] like Figure 3 As shown, each component of the output vector output from the light domain matrix device 200 is input into the corresponding threshold determiner 210 respectively. Figure 3 The x(t) and x(t+1) shown in FIG. 1 will be described in detail later.

[0076] Next, based on Figure 3 The optoelectronic hybrid computing device shown, back to Figure 1 , the threshold setting unit 122 in the setting module 120 is described in detail. The threshold setting unit 122 sets the threshold judgement device 210 corresponding to each component of the output vector of the light domain matrix device 200 based on the adjacency matrix K and the external field vector L output by the aforementioned problem conversion module 110. That is, the threshold setting unit 122 sets the threshold of the output channel of each component of the output vector based on the adjacency matrix K and the external field vector L, that is:

[0077]

Mathematical formula 4

[0078] T i =(Σ j K ij -L i ) / 2,

[0079] Then set the entire threshold vector T to Figure 3 In the threshold value judgement device 210 of the optoelectronic hybrid computing device shown in the figure. In the present embodiment 1, the threshold value judgement device 210 is set as a nonlinear threshold value judgement device. The threshold value judgement device 210 is used to compare the input value with the set threshold value. When the input value is greater than the threshold value, the threshold value judgement device 210 outputs 1, otherwise it outputs 0.

[0080] At this point, the processing of the setting module 120 is completed.

[0081] <Algorithm module 130>

[0082] The algorithm module 130 in the SAT problem processing system 100 is used to recursively solve the Ising problem converted by the problem conversion module 110 using the optoelectronic hybrid computing device encoded by the setting module 120. Figure 1 As shown, the algorithm module 130 includes an initialization unit 131 and a recursive solution unit 132 as its main structures.

[0083] Figure 4 is a flowchart of a recursive algorithm for solving the Ising problem according to the first embodiment. Figure 3 and Figure 4 , the recursive solution processing performed by the recursive solution unit 132 is specifically described.

[0084] First, the optoelectronic hybrid computing device is initialized by the initialization unit 131. Specifically, in step S1, the literal variable x of the Ising problem is initialized, the initial energy H is calculated, and the optimal energy Best_H = H, the optimal variable Best_x = x, the initial iteration number t = 0, and the maximum number of recursive iterations is set to Nmax. Then, proceed to step S2. 0 is initialized, and the initial energy H is calculated 0 , and the optimal energy Best_H = H is preset 0 , the optimal variable Best_x = x 0 , the initial iteration number t = 0, and the maximum number of recursive iterations is set to Nmax. Then, proceed to step S2.

[0085] Next, in step S2, based on the initialized optoelectronic hybrid computing device, the recursive solving unit 132 sets an iterative mathematical formula using a Gaussian noise vector, iterates the literal variable x, and calculates the corresponding energy H. The set iterative mathematical formula is as follows:

[0086]

Mathematical formula 5

[0087]

[0088] where x(t) is the variable value of the t-th iteration, x(t + 1) is the variable value of the (t + 1)-th iteration, is a Gaussian noise vector with a mean of 0 and a variance of s, and sign(x) is the sign function (set as x > 0, sign(x) = 1; x ≤ 0, sign(x) = 0). By using the Gaussian noise vector in this iterative mathematical formula, when solving using this algorithm, it can effectively jump out of the local optimal solution and thus obtain the global optimal solution. Then, proceed to step S3.

[0089] Next, in step S3, it is determined whether to update the optimal energy Best_H and the optimal literal variable Best_x according to the calculated energy H. Specifically, the calculated energy H is compared with the optimal energy Best_H. If H < Best_H, the optimal energy Best_H and the optimal literal variable Best_x are updated, set as Best_H = H, Best_x = x; if H ≥ Best_H, Best_H and Best_x remain unchanged, and the iteration number t is incremented by 1. Then, proceed to step S4.

[0090] Next, in step S4, it is determined whether the iteration number t is less than or equal to the maximum iteration number Nmax. If t < Nmax, return to step S2 to continue the iterative process; if t > Nmax, proceed to step S5, output the optimal literal variable Best_x and the optimal energy Best_H, and end the process.

[0091] So far, the iterative process performed by the recursive solving unit 132 is completed, and the optimal solution of the SAT problem is obtained.

[0092] The SAT problem processing system 100 involved in the first embodiment of the present invention is described above. According to the SAT problem processing system 100 involved in the first embodiment, by retaining binary or ternary clauses when preprocessing the CNF paradigm of the SAT problem to be solved, that is, converting an arbitrary CNF paradigm of the SAT problem to be solved into a CNF paradigm with binary or ternary clauses, it is possible to minimize the introduction of auxiliary variables when constructing the QUBO problem described later, thereby further avoiding the expansion of the scale of the SAT problem.

[0093] In addition, according to the SAT problem processing system 100 involved in the present embodiment 1, by setting a setting module 120 including a matrix core architecture setting unit 121 and a threshold setting unit 122, and using the matrix core architecture setting unit 121 in the setting module 120 to set the optical domain matrix device for realizing the matrix multiplication function of the optical domain in the optoelectronic hybrid computing device, and using the threshold setting unit 122 to set the threshold judgement device in the optoelectronic hybrid computing device, the advantages of high parallelism, low latency and low energy consumption in the matrix operation of the optoelectronic hybrid computing device can be utilized to solve the SAT problem efficiently and quickly. That is, compared with the traditional CPU / GPU, the matrix operation capability is 2 to 3 orders of magnitude faster, so that the problem that the solution time in the deterministic algorithm increases exponentially with the increase of the problem scale can be solved, and it is suitable for solving large-scale SAT problems.

[0094] In addition, according to the SAT problem processing system 100 involved in this embodiment 1, by utilizing Gaussian noise vectors in the processing performed by the algorithm module 130, it is possible to effectively jump out of the local optimal solution and obtain the global optimal solution, that is, it is possible to solve the problem of slow convergence speed in the random search algorithm, easy to fall into the local optimal solution and thus unable to find the global optimal solution.

[0095] Implementation Method 2

[0096] Implementation method 2 relates to a SAT problem processing method. Figure 5 Flowchart of the SAT problem processing method according to Embodiment 2 of the present invention. Figure 5 The flowchart shown in the figure describes in detail the SAT problem processing method involved in this embodiment 2. In addition, the SAT problem processing method is implemented by the SAT problem processing system involved in the embodiment 1. In the following description, in order to simplify the description, only the steps of the SAT problem processing method are briefly described, and some contents related to the embodiment 1 are omitted. However, the relevant contents recorded in the embodiment 1 can all be applied to the SAT problem processing method of this embodiment 2.

[0097] First, in step S11, the SAT problem to be solved is preprocessed to obtain a CNF paradigm with binary clauses or ternary clauses. Specifically, for any SAT problem to be solved, assuming that C i is the i-th clause in its CNF form, and C i is a unit clause, then C i =x j or Among them, x j represents the jth word, Indicates the jth character x j negation.

[0098] Obviously, x in the unit clause j The solution is unique. That is, only x j =1 or x j = 0 to make C i = 1. Get x j After finding the only solution of j Substitute the value into all the j If the clause is 1, eliminate the corresponding clause. If it is not certain whether the clause is satisfied, eliminate x in the clause. j Variable. Further, for the CNF paradigm after eliminating the unique solution variable, convert the polynomial clauses with more than 3 characters into ternary clauses, and retain the binary or ternary clauses originally existing in the CNF paradigm. After obtaining the CNF paradigm with binary or ternary clauses, proceed to step S12.

[0099] Next, in step S12, a QUBO problem is constructed based on the CNF paradigm with binary or ternary clauses. Specifically, for each clause C in the CNF paradigm processed by the preprocessing unit 111, i Construct a clause objective function φ(C i ). Then find the total objective function of the entire CNF paradigm and rewrite it as the objective function of the QUBO problem. Then, proceed to step S13.

[0100] Next, in step S13, the obtained QUBO problem is converted into the Hamiltonian function form of the Ising problem, thereby deriving the adjacency matrix K and the external field vector L of the Ising problem. Specifically, by introducing the spin variable, the objective function of the QUBO problem is rewritten into the Hamiltonian function form of the Ising problem, and the adjacency matrix K and the external field vector L of the Ising problem are derived, and then the process proceeds to step S14.

[0101] Next, in step S14, the light domain matrix for realizing the matrix multiplication function of the light domain is set based on the adjacency matrix K obtained in step S13. The result of the matrix-vector multiplication is obtained by using the set light domain matrix, and then the process proceeds to step S15.

[0102] Next, in step S15, the threshold value judgement device in the optoelectronic hybrid computing device is set based on the adjacency matrix K and the external field vector L. The optoelectronic hybrid computing device here has the same structure as the optoelectronic hybrid computing device described in embodiment 1. Specifically, based on the adjacency matrix K and the external field vector L of the Ising problem obtained in step S13, the threshold value of the channel output by each component of the output vector of the optical domain matrix device is set, and the entire threshold value vector is set in the threshold value judgement device of the optoelectronic hybrid computing device. Then proceed to step S16.

[0103] Next, in step S16, the optoelectronic hybrid computing device obtained after the settings in steps S14 and S15 is initialized.

[0104] Next, the process proceeds to step S17 , in which an iterative mathematical formula for recursive solution is set using a Gaussian noise vector, and iterative calculation is performed, and then the process proceeds to step S18 .

[0105] In step S18, it is determined whether the number of iterations is less than the maximum number of iterations. If the number of iterations is less than the maximum number of iterations, the process returns to step S17 to continue the iterative process; if the number of iterations reaches the maximum number of iterations, the optimal text variable and the optimal energy are output, and the process ends.

[0106] The above steps S16 to S19 correspond to steps S1 to S5 described in Implementation Example 1, and the specific contents described in steps S1 to S5 described in Implementation Example 1 can all be applied to steps S16 to S19 of Implementation Example 2.

[0107] According to the SAT problem processing method involved in this embodiment 2, by retaining binary or ternary clauses when pre-processing the CNF paradigm of the SAT problem to be solved, an arbitrary CNF paradigm of the SAT problem to be solved is converted into a CNF paradigm with only binary or ternary clauses, thereby minimizing the introduction of auxiliary variables when constructing the QUBO problem described later, thereby further avoiding the expansion of the scale of the SAT problem.

[0108] In addition, according to the SAT problem processing method involved in this embodiment 2, the optical domain matrix device for realizing the optical domain matrix multiplication function in the optoelectronic hybrid computing device is set according to the adjacency matrix K and the external field vector L of the Ising problem derived corresponding to the SAT problem to be solved, and the threshold value judgement device in the optoelectronic hybrid computing device is set, so that the advantages of high parallelism, low latency and low energy consumption of the optoelectronic hybrid computing device in matrix operation can be utilized to solve the SAT problem efficiently and quickly. That is, compared with the traditional CPU / GPU, the matrix operation capability is 2 to 3 orders of magnitude faster, so that the problem that the solution time in the deterministic algorithm increases exponentially with the growth of the problem scale can be solved, and it is suitable for solving large-scale SAT problems.

[0109] In addition, according to the SAT problem processing method involved in this embodiment 2, by using Gaussian noise vectors in the iterative mathematical formula for iterative calculation, it is possible to effectively avoid jumping out of the local optimal solution and obtain the global optimal solution. That is, it is possible to solve the problem of slow convergence speed and easy falling into the local optimal solution in the random search algorithm, thereby failing to find the global optimal solution.

[0110] The SAT problem processing system and method involved in the present invention are described above. However, the structure or steps shown in the above embodiment are only examples of the content of the present invention, and can be combined with other known technologies, or part of the structure can be omitted or changed within the scope of the gist of the present invention.

[0111] The present invention can freely combine the various embodiments, modify any structural elements of the various embodiments, or omit any structural elements of the various embodiments within the scope of the invention.

Claims

1. A SAT problem processing system, using an optoelectronic hybrid computing device including an optical domain matrix device and a threshold value judgement device for processing, characterized in that: include: A problem conversion module, which obtains an adjacency matrix and an external field vector associated with a CNF paradigm of the SAT problem based on the characteristics of the Ising problem; A setting module, which sets the light domain matrix device and the threshold value determiner according to the adjacency matrix and the external field vector; as well as An algorithm module is used to determine the optimal solution of the SAT problem through the light domain matrix and the threshold value determiner.

2. The SAT problem processing system according to claim 1, characterized in that: The problem conversion module simplifies the CNF paradigm of the SAT problem, constructs the QUBO problem using the simplified CNF paradigm, and then converts the QUBO problem into the Hamiltonian function form of the Ising problem, thereby deriving the adjacency matrix and the external field vector.

3. The SAT problem processing system according to claim 2, characterized in that: The problem conversion module implements the simplification by preprocessing the CNF paradigm, wherein the preprocessing includes converting a polynomial clause having a number of literal variables greater than 3 into a ternary clause.

4. The SAT problem processing system according to any one of claims 1 to 3, characterized in that: The setting module sets the threshold determiner corresponding to each component of the output vector of the light domain matrix device based on the adjacency matrix and the external field vector.

5. The SAT problem processing system according to claim 1, characterized in that: The threshold determiner is a non-linear threshold determiner.

6. The SAT problem processing system according to claim 1, characterized in that: The algorithm module uses a Gaussian noise vector to set an iterative mathematical formula, performs a recursive solution through the iterative mathematical formula, and then determines the optimal solution.

7. The SAT problem processing system according to claim 6, characterized in that: The text variables of the SAT problem are iterated using the iterative mathematical formula, and the optimal energy and the optimal text variables are determined according to the energy obtained in each iteration until a preset maximum number of iterations is reached.

8. A method for processing a SAT problem, using an optoelectronic hybrid computing device including an optical domain matrix device and a threshold value judgement device for processing, characterized in that: include: A problem transformation step, in which, based on the characteristics of the Ising problem, an adjacency matrix and an external field vector associated with the CNF normal form of the SAT problem are obtained; A setting step, in which the light domain matrix device and the threshold value determiner are set according to the adjacency matrix and the external field vector; as well as Algorithm step, in which the optimal solution of the SAT problem is determined by the light domain matrix device and the threshold value determiner.

9. The SAT problem processing method according to claim 8, characterized in that: In the problem conversion step, the CNF paradigm of the SAT problem is simplified by preprocessing the CNF paradigm. The preprocessing includes converting a polynomial clause having a number of literal variables greater than 3 into a ternary clause.

10. The SAT problem processing method according to claim 8 or 9, characterized in that: In the setting step, the threshold determiner corresponding to each component of the output vector of the light domain matrix device is set based on the adjacency matrix and the external field vector.

11. The SAT problem processing method according to claim 8, characterized in that: In the algorithm step, a Gaussian noise vector is used to set an iterative mathematical formula, and a recursive solution is performed through the iterative mathematical formula to determine the optimal solution.

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