How to define school security problems

First step in solving a problem is figuring out if the issue is "solvable", "unsolvable", "resource-constrained", or even "ill-defined".

There are lots of different approaches to solving problems. Some people like to throw ideas at the wall and see what sticks. Others have a gut feeling about a solution and follow that. In the field of computer science, the first step in problem solving is defining the classification of the problem because problems aren’t all the same.

Classification of problem types originates from the foundational work in computability theory and complexity theory in the early 20th century. Mathematicians like Alan Turing, Alonzo Church, and Kurt Gödel laid the groundwork by exploring what kinds of problems the early computers could solve. Turing’s concept of the “Turing machine” in 1936 introduced the idea of decidable vs. undecidable problems. This created theories like “the Halting Problem” that cannot be solved by any algorithm.

The Halting Problem asks whether it’s possible to create an algorithm that can determine if any given computer input will cause a program to eventually stop (halt) or continue to run forever. With this experiment, Turing proved there is no universal algorithm that can exist which makes this problem “unsolvable”. This early theory and test proved the inherent limits to what computers can solve regardless of how powerful they are.

What’s a Halting Problem for School Security?

The essence of the Halting Problem is that more resources can’t solve something that is inherently unsolvable. This is like the problem Dallas ISD faced when they invested a huge amounts of resources into physical security after a shooting inside a classroom in 2024, and then there was another shooting at the same school in 2025.

Dallas ISD high schools have metal detectors, school police officers, security screenings, ballistic shields, lockdown alert systems, campus security audits, and clear backpack requirements. This didn’t stop a student from being shot inside a classroom at Wilmer-Hutchins High School on April 12, 2024.

Yesterday, three students were shot and another was injured when a 17-year-old student opened fire inside Wilmer-Hutchins High School during afternoon classes. The shooter fled before police arrived on campus. During a press conference, the police chief said "it was not a failure of our staff, of our protocols, or of the machinery that we have". (Second shooting at same school shows why TSA-style security doesn't work)

Problem: Students are able to sneak guns into a huge school that has dozens of doors and hundreds of windows on a 2 million sq/ft campus.

Failed Solution: Add more physical security and guards.

Problem Classification: Unsolvable, Resource-Constrained, and/or Ill-Defined

Why did Dallas ISD fail? There are many reasons, but the first one is they didn’t take time to think about how to classify the problem.

More About Problem Classification

As computing matured, researchers began categorizing problems by how efficiently they could be solved. This created the concept of tractable vs. intractable problems. These classifications help computer scientists understand which problems are feasible and which are fundamentally beyond computational reach regardless of how many resources are dedicated to solving them.

Over time, more practical classifications like resource-constrained or constraint-satisfaction problems were developed to describe real-world applications like optimizing logistics, cybersecurity, and AI development.

Computer science problems can fall into one or multiple of these categories. As technology or knowledge advances and circumstances change, the classification of a problem can move in either direction (because new tech can be used for good or bad to make things either easier or harder).

• Solvable Problems: Problems that can be solved by an algorithm that always produces a correct answer for every valid input (e.g., sorting, shortest paths).

• Partially Solvable (Semi-Decidable) Problems: Problems where an algorithm may confirm a solution if it exists but might run forever if it doesn't (e.g., Halting Problem).

• Unsolvable Problems: Problems for which no algorithm can solve all possible inputs (e.g., Halting Problem, Post’s Correspondence Problem).

• Resource-Constrained Problems: Problems that are solvable in theory but not in practice due to time, memory, or computational power limits (e.g., brute-force decryption, large-scale TSP).

• Tractable vs Intractable Problems: Tractable problems can be solved in polynomial time, while intractable ones require exponential or worse time as input size grows (e.g., NP-hard problems).

• Well-Defined vs Ill-Defined Problems: Well-defined problems have clear goals and rules (e.g., Sudoku), while ill-defined ones involve ambiguity or subjective criteria (e.g., winning at poker against players who are bluffing).

• Constraint-Satisfaction Problems: Problems that involve finding solutions that meet a set of specific constraints (e.g., scheduling, delivery cost vs. time route optimization).

Applying Problem Types to School Safety

Problems that schools try to solve for improving security can range across the entire spectrum of computer science problem types.

Going back to the shootings at Wilmer-Hutchins High School in Dallas, preventing a student from carrying a gun into the school building is a “resource-constrained” problem because in theory there could be multiple guards with metal detectors at every single door (dozens on campus) and the hundreds of ground level windows could all be unbreakable ballistic glass, but implementing this kind of physical security at scale is impractical.

An “unsolvable problem” is predicting if a student will actually commit a school shooting based on a threat that’s posted online. Before a school shooting threat assessment process starts, a threat made online exists in a state of ontological ambiguity. The state of the threat isn’t unknown, the problem is that the binary categories of real and hoax have no fixed meaning yet. This is a superposed epistemic state, where all possible realities coexist as potentialities. Each threat starts by existing as both a real danger and a hoax at the same time (read more: When is a school shooting threat real?).

Schools need to classify problems to avoid the same traps that computer scientists try to avoid. If a problem is unsolvable, intractable, or ill-defined, throwing more resources at the problem is just a waste of time and money.

First Principles of Impossible Problems

If a problem seems impossible to solve, either the problem is being classified incorrectly, the wrong problem is being defined, or the wrong set of solutions are being applied to it.

First principles thinking is a foundational problem-solving approach embraced by the most successful Silicon Valley billionaires. It involves breaking down complex problems into their most basic, fundamental truths and reasoning up from there. This approach enables innovative solutions by challenging the status quo and encouraging fresh perspectives.

The core problem for school safety is how do we prevent people—students, staff, and community members—from being shot on school campuses?

The three most foundational elements are:

1. Someone is motivated to cause harm.

2. That person can access a gun.

3. A school campus is an open and accessible public place that people use every day.

If a student is motivated to cause harm and can get a gun, it’s easy for the student to take the gun to a school.

From a first-principles standpoint, you can think of a school shooting as the combination of these elements. If any of the three is disrupted—(1) the individual’s motivation toward violence is changed, (2) access to firearms is significantly constrained, or (3) the open-school environment is restructured—the likelihood of a school shooting happening decreases dramatically.

Using 'first principles' thinking to decrease school shootings by 10x

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David Riedman is the creator of the K-12 School Shooting Database, Chief Data Officer at a global risk management firm, and a tenure-track professor. Listen to my weekly podcast—Back to School Shootings—or my recent interviews on Freakonomics Radio, New England Journal of Medicine, and my article on CNN about AI and school security.