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If I steal someone's algorithm, how would anyone be able to prove that I am using their algorithm? Only I have access to the code for the algorithm?

Unless someone sees my code, they can't say what algorithm is actually being executed?

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George White's answer succinctly gives an answer to this question in its context, the only thing I could add from a more technical perspective, since I sense there is some curiosity from that angle is that:

You can only patent algorithms in a coupled with other tangible components as part of a system, method or computer program product, and not merely the algorithm itself, and that only. It may seem a technicality, but I sense this questions taps into that, and it is, in fact, an important consideration: Not seeing your code does not mean one is unable to define the process flow of software.

For example: If, upon approaching my car's door a camera coupled with all the necessary hardware and software to verify its me, opens or unlocks the door, from a patent perspective, if the method of opening a car door in this way (or the system comprising of all the hardware and software components for this) is able to do this as such as is described in a granted patent (or potentially a provisional patent) if the necessary components of the system, including a process flow of the software, regardless if the code itself is written or even structured differently (this is not copyright!), if it actually goes through the same steps generally defined in a patent application, for example, in a flow chart or verbally described step by step, it will be a patent infringement still.

In some cases this can be proven merely by what the software does. Even simply wedging in extra steps in the process flow that does not substantially improve, and neither does it worsen or impair the software component, it will likely be violative any ways.

But, generally, it all comes down to the steps set forth in the software component: If those match, and it can be, with reasonable probability, proven that they are infringing, the actual way the code is written and/or structured is a distinction without a difference in the eye of patent law, a suit can be merited, and the steps may ensue that George White described on court.

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    It is true that that, in some cases, the details of the code may not be required to judge infringement if a claim. It depends on the claim. Patents do not cover results but the specific apparatus or steps that achieve results. In the example of a car that unlocks itself based on visual information, a claim might or might not be specific to the way images are judged. One method might use face recognition and another might use recognition of gait. It might or might not be readily apparent without opening up the software which is being used and the claim in question could be specific.
    – George White
    Jan 2 at 17:41
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    Adding a step to make a non-infringing improvement is flat wrong. If you have all the steps of a claim, adding other steps can’t make your product non-fringing. Removing a step can avoid infringement but never adding a step. Two smaller points are that it is misleading to suggest that a patent application is judged by “improvement” over something else. Improvement is not a criteria for patentability. Last, the word “anticipate” has a technical meaning in patent law that relates to novelty and it is being used here in a context of obviousness. They are quite different concepts.
    – George White
    Jan 2 at 17:57
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    Generally, whether something is useful or not is not a matter of patentability, and therefore the degree of relative usefulness to prior art should also not be a matter of consideration, but in specific cases: It is. When justifying the lack of obviousness as a result of combining, as it is most typical, multiple inventions, an examiner may be compelled to arguing as to why one would combine certain prior arts which typically, more often than not, comes down to a debate around the objective as to why one would combine certain prior arts, and there, improvement is a key and central question as Jan 2 at 20:38
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    I agree that the concept of improvement can be a factor in an obviousness analysis regarding motivation to combine. In other comments I think you may be conflating infringement and patentability. The patentability of something is irrelevant to the question of infringement. If all steps of an issued patent are present then there is infringement - period. It is irrelevant if added steps make the new product patentable or not. This is a frequent confusion. Patenting your invention does not provide immunity from infringing an earlier invention that yours is a proper superset of.
    – George White
    Jan 2 at 21:26
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    No - removing a step would create something that does not infringe. I understood you to suggest that adding a step could also lead to non infringement. Replacing a step would not infringe unless under the doctrine of equivalents. You are still focused on non obviousness. It is only an issue when determining patentability not infringement. In judging if replacing B with D removed infringement we do not judge anything about obviousness, only equivalence under the DOE.
    – George White
    Jan 3 at 0:54
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In civil lawsuits, including patent infringement,there is something called discovery where a judge requires the defendant to expose information relevant to the case to the plaintive.

Also, patent owners can attempt to reverse-engineer products to look for infringement. It is not only software. Integrated circuits can be analyzed by pealing away layers. https://electronics.stackexchange.com/questions/13472/is-it-possible-to-reverse-engineer-a-chip-design

See answer to similar question How is patent infringement usually being discovered?

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