Prosecution Insights
Last updated: April 19, 2026
Application No. 17/887,217

METHODS, SYSTEMS, AND MEDIA FOR RESOLVING DATABASE QUERIES USING ALGEBRAIC EXPRESSIONS USING MATRIX-MATRIX MULTIPLICATION

Final Rejection §101
Filed
Aug 12, 2022
Examiner
LE, MICHAEL
Art Unit
2163
Tech Center
2100 — Computer Architecture & Software
Assignee
Redis Ltd.
OA Round
7 (Final)
66%
Grant Probability
Favorable
8-9
OA Rounds
3y 3m
To Grant
88%
With Interview

Examiner Intelligence

Grants 66% — above average
66%
Career Allow Rate
568 granted / 864 resolved
+10.7% vs TC avg
Strong +22% interview lift
Without
With
+22.1%
Interview Lift
resolved cases with interview
Typical timeline
3y 3m
Avg Prosecution
61 currently pending
Career history
925
Total Applications
across all art units

Statute-Specific Performance

§101
12.4%
-27.6% vs TC avg
§103
52.7%
+12.7% vs TC avg
§102
13.4%
-26.6% vs TC avg
§112
15.9%
-24.1% vs TC avg
Black line = Tech Center average estimate • Based on career data from 864 resolved cases

Office Action

§101
DETAILED ACTION Summary and Status of Claims The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA . This Office Action is in response to Applicant’s reply filed 12/2/2025. Claims 1-24 are pending. Claims 1-24 are rejected under 35 U.S.C. 101. The text of those sections of Title 35, U.S. Code not included in this action can be found in a prior Office action. Claim Rejections - 35 USC § 101 35 U.S.C. 101 reads as follows: Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title. Claims 1-24 are rejected under 35 U.S.C. 101 because the claimed invention is directed to a judicial exception (i.e., a law of nature, a natural phenomenon, or an abstract idea) without significantly more. Pursuant to MPEP 2106, claims are analyzed using a two step process to determine whether they are directed to a judicial exception without significantly more. In step 1, Examiner must determine whether the claims belong to one of the statutory categories. In step 2A-1, Examiner must determine whether the claim is directed to a judicial exception. In step 2A-2, Examiner must determine whether the claims recite additional elements that integrate the judicial exception into a practical application. In step 2B, Examiner must determine whether the claims recite additional elements which amount to significantly more than the abstract idea. For step 2A-1, Claim 1 is directed to a method of resolving a database query comprising: (1) “building in computer memory an expression for a path having a plurality of edges and having a longest path length for a connected component in a query graph corresponding to the database query using a hardware processor, wherein the database query is a query to retrieve data from a graph database,” (2) “performing matrix-matrix multiplication on operands of the expression to provide a result using the hardware processor, wherein performing matrix-matrix multiplication on the operands of the expression comprises performing matrix-matrix multiplication on a first pair of the operands concurrently with performing matrix-matrix multiplication on a second pair of the operands,” (3) “providing a response to the database query based on the result,” (4) “wherein the building, the performing, and the providing eliminate linear traversal through the plurality of edges of the graph database,” (5) “wherein the matrix-matrix multiplication identifies relationships between a number of nodes in parallel to reduce a time associated with resolving the database query,” wherein building the expression for the path comprises: for each edge of the plurality of edges on the path (6) “if a source node of the edge is labelled, getting a label matrix represented by the source node of the edge and adding the label matrix as a right-most operand of the expression,” (7) “retrieving a representation type matrix represented by the source node of the edge,” (8) “adding the representation type matrix as a right most operand of the expression,” and (9) “for a last edge on the path, if a destination node of the last edge is labelled, adding a label matrix of the destination node of the last edge to the right most operand of the expression.” Examiner is required to give claim limitations their broadest reasonable interpretation in light of the specification. However, limitations from the specification are not read into the claims. MPEP 2111. Courts consider a mental process if it “can be performed in the human mind, or by a human using a pen and paper.” The mental process grouping covers concepts performed in the human mind, including observation, evaluation, judgment, and opinion. MPEP 2016(a)(2)(III). Additionally, the mathematical concepts grouping is defined as mathematical relationships, mathematical formulas or equations, and mathematical calculations. The Supreme Court has identified a number of concepts falling within this grouping as abstract ideas including: a procedure for converting binary-coded decimal numerals into pure binary form, Gottschalk v. Benson, 409 U.S. 63, 65, 175 USPQ2d 673, 674 (1972); a mathematical formula for calculating an alarm limit, Parker v. Flook, 437 U.S. 584, 588-89, 198 USPQ2d 193, 195 (1978); the Arrhenius equation, Diamond v. Diehr, 450 U.S. 175, 191, 209 USPQ 1, 15 (1981); and a mathematical formula for hedging, Bilski v. Kappos, 561 U.S. 593, 611, 95 USPQ 2d 1001, 1004 (2010). Limitations can also be deemed insignificant extra-solution activity (IESA). The term "extra-solution activity" can be understood as activities incidental to the primary process or product that are merely a nominal or tangential addition to the claim. Extra-solution activity includes both pre-solution and post-solution activity. An example of pre-solution activity is a step of gathering data for use in a claimed process, e.g., a step of obtaining information about credit card transactions, which is recited as part of a claimed process of analyzing and manipulating the gathered information by a series of steps in order to detect whether the transactions were fraudulent. An example of post-solution activity is an element that is not integrated into the claim as a whole, e.g., a printer that is used to output a report of fraudulent transactions, which is recited in a claim to a computer programmed to analyze and manipulate information about credit card transactions in order to detect whether the transactions were fraudulent. MPEP 2106.05(g). As noted by Applicant, “[g]raphs are mathematical structures that can model and indicate relationships between different objects or entities” and the nodes and edges of a graph can be stored or represented as matrices. Spec. at paras. 0003-0007. Therefore, it is interpreted that translating a node of a graph to a matrix is known. Further, as recited in the claim, the “algebraic expression using matrix-matrix multiplication” recites a mathematical concept, that includes at least mathematical relationships and mathematical calculations. MPEP 2106.04(a)(2)(I). Such a mathematical concept can be performed, as recited in the limitations of claim 1, as a mental process because it is a concept that can be performed in the human mind, including observation, evaluation, judgment, or opinion. MPEP 2106.04(a)(2)(III). “For example, in a claim that includes a series of steps that recite mental steps as well as a mathematical calculation, an examiner should identify the claim as reciting both a mental process and a mathematical concept for Step 2A, Prong One to make the analysis clear on the record.” MPEP 2106.04, subsection II.B. Under such circumstances, however, the Supreme Court has treated such claims in the same manner as claims reciting a single judicial exception. Id. (discussing Bilski v. Kappos, 561 U.S. 593 (2010)). As there are no bright lines between the types of judicial exceptions, and many of the concepts identified by the courts as exceptions can fall under several exceptions, MPEP 2106.04, subsection I instructs examiners to “identify . . . the claimed concept (the specific claim limitation(s) that the examiner believes may recite an exception) [that] aligns with at least one judicial exception.” In this case, limitations (1), (3), and (6) through (9) recite steps that are categorized as mental processes because they can be practically performed by a person in the mind or with the aid of pen and paper. For example, a person can observe and evaluate a query graph, the database query, and translate the nodes of the graph into their equivalent matrices, as recited. Limitation (2) recites a step of performing matrix-matrix multiplication, which is an abstract idea categorized as a mathematical calculation. Although, limitation (2) recites performing the calculations concurrently, such steps can be performed by a person with the aid of a computer as a tool to perform the concept (i.e., mathematical calculations), which does not provide an improvement to the technology. Limitations (4) and (5) seem to be recitations of conclusions or intended result without actually performing any steps. For at least these reasons, claim 1 is directed to observations of a graph structure and evaluations to build an algebraic expression and solve it, by performing mathematical calculations, to respond to a query, which can be performed in the human mind or by a human using a pen and paper or with the aid of a computer as a tool to perform the concept. The Federal court has “treated analyzing information by steps people go through in their minds, or by mathematical algorithms, without more, as essentially mental processes within the abstract idea category.” Elec. Power, 830 F.3d at 1354. Therefore, it is directed to an abstract idea categorized as a mental process. For step 2A-2, claims are analyzed to determine whether the claim as a whole integrates the recited judicial exception into a practical application of the exception. This evaluation is performed by (1) identifying whether there are any additional elements recited in the claim beyond the judicial exception, and (2) evaluating those additional elements individually and in combination to determine whether the claim as a whole integrates the exception into a practical application. See MPEP 2106.04(d). One way to determine integration into a practical application is when the claimed invention improves the functioning of a computer or improves another technology or technical field. To evaluate an improvement to a computer or technical field, the specification must set forth an improvement in technology and the claim itself must reflect the disclosed improvement. See MPEP 2106.04(d)(1). For much of the same reasons described above, claim 1 does not recite additional limitations that integrate the abstract idea into a practical application. Additional limitations that are indicative of integration into a practical application under MPEP 2106.04(d) include: improvements to the functioning of a computer, or any other technology or technical field; applying the judicial exception with, or by use of, a particular machine; effecting a transformation or reduction of a particular article to a different state or thing; and applying or using the judicial exception in some other meaningful way beyond generally linking the use of the judicial exception to a particular technological environment, such that the claim as a whole is more than a drafting effort designed to monopolize the exception. In contrast, limitations that are not indicative of “integration into a practical application” include: adding the words “apply it” or equivalent; adding insignificant extra solution activity to the judicial exception; and generally linking the use of the judicial exception to a particular technological environment or field of use. In consideration of the limitations of claim 1, none of the limitations fall under the types of limitations indicative of integration into a practical application as enumerated above. The building and solving of an algebraic expression for a path for a connected component of a graph to respond to a query, as recited, do not adequately convey any type of improvement, transformation, or application that would provide meaningful limits on the abstract idea. At best, the limitations merely link the abstract idea to graph database technologies. This type of limitation merely confines the use of the abstract idea to a particular technological environment (e.g., graph database technology) and thus fails to integrate the abstract idea into a practical application/add an inventive concept to the claims. See MPEP 2106.04(d). Similarly, the steps for building the algebraic expression merely take advantage of the mathematical concepts for representing a graph using matrices. As far as performing the matrix-matrix calculations of limitation (2), the limitation provides nothing more than mere instructions to implement an abstract idea on a generic computer, which is capable of performing mathematical calculations concurrently. See MPEP 2106.05(f). MPEP 2106.05(f) provides the following considerations for determining whether a claim simply recites a judicial exception with the words “apply it” (or an equivalent), such as mere instructions to implement an abstract idea on a computer: (1) whether the claim recites only the idea of a solution or outcome i.e., the claim fails to recite details of how a solution to a problem is accomplished; (2) whether the claim invokes computers or other machinery merely as a tool to perform an existing process; and (3) the particularity or generality of the application of the judicial exception. Thus, for at least these reasons, claim 1 does not recite limitations that integrate the abstract idea into a practical application. With regards to the added limitations of “computer memory”, “using a hardware processor,” and “a graph database,” these limitations are of computer components, which are recited at a high level of generality and do not provide meaningful limits on the abstract idea. For step 2B, claims are analyzed to determine whether the claim as a whole amounts to significantly more than the recited exception i.e., whether any additional element, or combination of additional elements, adds an inventive concept to the claim. See MPEP 2106.05. For much of the same reasons discussed above in regards to step 2A-2, the limitations recited in claim 1 do not amount to significantly more than the abstract idea. Limitation (2) is at best mere instructions to “apply” the abstract idea of mathematical calculations, which cannot be an inventive concept. See MPEP 2106.05(f). The remaining limitations, as discussed above, recite steps for translating a graph into its mathematical matrix equivalent, which as described by Applicant’s specification, is known. Limitations (4) and (5), as noted above, seem to be mere statements of conclusion without actually performing any steps or features. As a result, claim 1 is directed to an abstract idea without significantly more. Claim 2 Pursuant to step 2A, part 1, claim 2 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 2 recites the additional limitations of for each edge on the path when building the expression for the path, if the edge is reversed, swapping a designation of a source node for the edge and a designation of a destination node for the edge. These additional limitations merely add an additional evaluation step that can be performed by a person in the mind. By recognizing that the edge is reversed, the person can switch the source and destination nodes, and accordingly, translate them to their corresponding matrices as appropriate. Therefore, For much of the same reasons as described above, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claim 3 Pursuant to step 2A, part 1, claim 3 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 3 recites the additional limitations of or each edge on the path when building the expression for the path, if the edge is reversed, transposing the representation type matrix. These additional limitations take advantage of the fact that source nodes are represented in rows and destination nodes are represented in columns. Spec. at para. 0006. Thus, a person evaluating the graph to translate the nodes to their mathematical matrix equivalent, would recognize the reversed edge and transpose the representation matrix of the source node, thereby making it a destination node. Therefore, for much of the same reasons discussed above, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claims 4 Pursuant to step 2A, part 1, claim 4 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 4 recites the additional limitations of dividing the query graph into a plurality of connected components which includes the connected component. These additional limitations can be practically performed by a person in the mind or with the aid of pen and paper by observing the query graph and dividing it as desired to create a plurality of connected components. Therefore, for much of the same reasons as discussed above, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claim 5 Pursuant to step 2A, part 1, claim 5 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 5 recites the additional limitations of wherein the connected component is a disjoint search pattern. These additional limitations merely describe the type of data to be manipulated and processed, which is mere insignificant extra solution activity. MPEP 2106.05(g). Therefore, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claim 6 Pursuant to step 2A, part 1, claim 6 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 6 recites the additional limitations of wherein the connected component has a length greater than or equal to any other connected component in the query graph. These additional limitations describe the type of data that is selected to be manipulated, which is insignificant extra solution activity. MPEP 2106.05(g). Therefore, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claim 7 Pursuant to step 2A, part 1, claim 7 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 7 recites the additional limitations of wherein the longest path length is a path length that is larger than any other path length for the query graph, and the path length is a count of consecutive edges traversed in the query graph without revisiting a node. These additional limitations describe the type of data to be selected for processing and manipulation, which is insignificant extra solution activity. MPEP 2106.05(g). Therefore, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claim 8 Pursuant to step 2A, part 1, claim 8 depends on claim 1 and therefore recites the same abstract idea. Pursuant to step 2A, part 2, claim 8 recites the additional limitations of removing from the connected component: all edges of the path; and then any nodes in the path that have no remaining connected edges. These additional limitations also recite a step of observation and evaluation that can be performed by a person in the mind or with the aid of pen and paper, and are also directed at selecting data to be manipulated, which is insignificant extra solution activity on its own. Therefore, these additional limitations do not integrate the abstract idea into a practical application. Pursuant to step 2B, the additional limitations do not amount to significantly more than the abstract idea because the limitations are not recited in a manner that provides improvements to the functioning of a computer or any other technology or technical field. Claims 9-16 are essentially the same as claims 1-8, respectively, in the form of a system. Therefore, they are rejected for the same reasons. Claims 9-16 further recite the additional limitations of a “memory” and a “hardware processor”. However, these additional limitations reciting computer components are recited at a high level of generality that does not put meaningful limits on the abstract idea. Therefore, they do not integrate the abstract idea into a practical application nor do they amount to significantly more than the abstract idea. Claims 17-24 are essentially the same as claims 1-8, respectively, in the form of a non-transitory computer readable medium. Therefore, they are rejected for the same reasons. Claims 17-24 further recite the additional limitations of a “non-transitory computer readable medium” and a “processor”. However, these additional limitations reciting computer components are recited at a high level of generality that does not put meaningful limits on the abstract idea. Therefore, they do not integrate the abstract idea into a practical application nor do they amount to significantly more than the abstract idea. For the reasons explained above, claims 1-24 are rejected because they are directed to an abstract idea without significantly more. To expedite a complete examination of the instant application, the claims rejected under 35 U.S.C. 101 (nonstatutory) above are further rejected as set forth below in anticipation of applicant amending these claims to place them within the four statutory categories of invention. Response to Arguments Rejection of claims 1-24 under 35 U.S.C. 101 Applicant’s arguments in regards to the rejections to claims 1-24 under 35 U.S.C. 101, have been fully considered but they are not persuasive. In regards to claim 1, Applicant argues the claim is directed to patent eligible subject matter because (1) the claim recites “performing matrix-matrix multiplication on a first pair of operands concurrently with performing matrix-matrix multiplication on a second pair of operands,” (2) “the building, the performing, and the providing eliminate linear traversal through the plurality of edges of the graph database,” and (3) “the matrix-matrix multiplication identifies relationships between a number of nodes in parallel to reduce a time associated with resolving the database query.” Remarks at 8-9. Examiner is required to give claim limitations their broadest reasonable interpretation in light of the specification. However, limitations from the specification are not read into the claims. MPEP 211. Applicant does not seem to present arguments with regards to the limitations for step 2A-1. Therefore, Examiner asserts the limitations are directed to an abstract idea categorized under mental processes. In regards to limitations (1) and (3), Applicant argues the performed actions “concurrently” and “in parallel” improves computer related technology because it reduces latencies associated with traversal of the graph, reducing power consumption, increasing processing, and providing faster response times to the database query. Remarks at 9. Examiner respectfully disagrees. Simply improving the speed and efficiency of mathematical calculations is not an improvement to the technology. These limitations are essentially “claiming the improved speed or efficiency inherent with applying the abstract idea on a computer,” which does not integrate the abstract idea into a practical application nor provide an inventive concept. Intellectual Ventures I LLC v. Capital One Bank (USA), 792 F.3d 1363, 1367, 115 USPQ2d 1636, 1639 (Fed. Cir. 2015). In regards to limitation (2), Applicant argues the limitation recites a step that reduces the amount of time required to resolve the database query, thereby improving the functioning of the database. Remarks at 9. Examiner respectfully disagrees. While the limitation recites the steps “eliminate linear traversal through the plurality of edges of the graph database,” the limitation, and remainder of the claim, do not recite specifics that demonstrate the asserted improvement. As explained in the rejection above, the limitation is merely a recitation of intended result. The steps of “building,” “performing”, and “providing” do not recite steps that demonstrate the asserted improvement. In particular, the “building” simply traverses a path in the graph to build the expression, the ”performing” simply performs the mathematical calculations (i.e., the matrix-matrix multiplication), and the “providing” simply returns the query response. None limitations, as recited, adequately demonstrate the asserted improvement. Accordingly, the limitations of the claims do not integrate the abstract idea into a practical application. In regards to step 2B, Applicant does not present specific arguments. Therefore, Examiner asserts, for much of the reasons explained above, the limitations do not amount to significantly more than the abstract idea. Applicant does not present any arguments with regards to the remaining claims. Therefore, they remain rejected for at least the same reasons. For at least these reasons, claims 1-24 are directed to an abstract idea, categorized under mathematical concepts and mental processes, without significantly more. Consequently, the rejection to claims 1-24 under 35 U.S.C. 101 is maintained. Additional Prior Art Additional relevant prior art are listed on the attached PTO-892 form. Some examples are: Zhu (US Patent 5,490,608) discloses a system and method for tree reduction using matrix multiplication constructed from parsing nodes in the tree. Conclusion THIS ACTION IS MADE FINAL. Applicant is reminded of the extension of time policy as set forth in 37 CFR 1.136(a). A shortened statutory period for reply to this final action is set to expire THREE MONTHS from the mailing date of this action. In the event a first reply is filed within TWO MONTHS of the mailing date of this final action and the advisory action is not mailed until after the end of the THREE-MONTH shortened statutory period, then the shortened statutory period will expire on the date the advisory action is mailed, and any extension fee pursuant to 37 CFR 1.136(a) will be calculated from the mailing date of the advisory action. In no event, however, will the statutory period for reply expire later than SIX MONTHS from the mailing date of this final action. Any inquiry concerning this communication or earlier communications from the examiner should be directed to Examiner Michael Le whose telephone number is 571-272-7970 and fax number is 571-273-7970. The examiner can normally be reached Mon-Fri 9:30 AM – 6 PM. Examiner interviews are available via telephone, in-person, and video conferencing using a USPTO supplied web-based collaboration tool. To schedule an interview, applicant is encouraged to use the USPTO Automated Interview Request (AIR) at http://www.uspto.gov/interviewpractice. If attempts to reach the examiner by telephone are unsuccessful, the examiner’s supervisor, Tony Mahmoudi can be reached on 571-272-4078. The fax phone number for the organization where this application or proceeding is assigned is 571-273-8300. Information regarding the status of published or unpublished applications may be obtained from Patent Center. Unpublished application information in Patent Center is available to registered users. To file and manage patent submissions in Patent Center, visit: https://patentcenter.uspto.gov. Visit https://www.uspto.gov/patents/apply/patent-center for more information about Patent Center and https://www.uspto.gov/patents/docx for information about filing in DOCX format. For additional questions, contact the Electronic Business Center (EBC) at 866-217-9197 (toll-free). If you would like assistance from a USPTO Customer Service Representative, call 800-786-9199 (IN USA OR CANADA) or 571-272-1000. /MICHAEL LE/Examiner, Art Unit 2163 /TONY MAHMOUDI/Supervisory Patent Examiner, Art Unit 2163
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Prosecution Timeline

Aug 12, 2022
Application Filed
Jul 29, 2023
Non-Final Rejection — §101
Nov 07, 2023
Response Filed
Feb 28, 2024
Non-Final Rejection — §101
Jun 06, 2024
Response Filed
Jun 15, 2024
Final Rejection — §101
Aug 21, 2024
Response after Non-Final Action
Sep 23, 2024
Request for Continued Examination
Sep 25, 2024
Response after Non-Final Action
Sep 30, 2024
Non-Final Rejection — §101
Jan 02, 2025
Response Filed
Apr 19, 2025
Final Rejection — §101
Jun 24, 2025
Response after Non-Final Action
Jul 02, 2025
Request for Continued Examination
Jul 08, 2025
Response after Non-Final Action
Aug 09, 2025
Non-Final Rejection — §101
Dec 02, 2025
Response Filed
Mar 25, 2026
Final Rejection — §101 (current)

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Expected OA Rounds
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3y 3m
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