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--- compai [2024/10/13 22:57] – [Conclusions] pedroortega
+++ compai [2026/05/23 10:07] (current) – [Computation is deduction, pattern recognition is induction] pedroortega
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 **Deduction** is the method which yields inevitable conclusions based on given premises and rules. The archetypal example is that if you know "all humans are mortal" (premise) and "Socrates is a human" (premise), then you can unequivocally conclude that "Socrates is mortal" (necessary conclusion) through the use of a [[https://en.wikipedia.org/wiki/Syllogism|categorical syllogism]] (rule).
-**Induction:** This method produces general hypotheses (rules & premises for instance) derived from specific observations. An example is observing that the sun has risen every day in recorded history and thus concluding that the sun will rise every day (a general rule, but not an absolute certainty). Another example would be to observe that "Socrates is mortal" and then conclude that this is because "all humans are mortal" and "Socrates is a human", although the credence attributed to this hypothesis is arguably quite low given the anecdotal data. Induction is often criticized because unlike deduction, it does not lead to a single conclusion, but multiple possible explanations.
+**Induction:** This method produces general hypotheses (rules & premises for instance) derived from specific observations. An example is observing that the sun has risen every day in recorded history and thus concluding that the sun will rise every day (a general rule, but not an absolute certainty). Another example would be to observe that "Socrates is mortal" and then conclude that this is because "all humans are mortal" and "Socrates is a human", although the credence attributed to this hypothesis is arguably quite low given the anecdotal data. Induction is often criticized because unlike deduction, it does not lead to a single conclusion, but multiple possible explanations. Singling out any particular explanations thus //adds// information to the argument.
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 ===== Induction and the computational complexity classes =====
-The above results apply to the limit case when we have unlimited resources to run and invert programs. But similar results hold when take into account computational complexity. In fact, the relationship between deterministic and nondeterministic complexity classes mirrors the divide between deduction and induction.
+The above results apply to the limit case when we have unlimited resources to run and invert programs. But similar results hold when we take into account computational complexity. In fact, the relationship between deterministic and nondeterministic complexity classes mirrors the divide between deduction and induction.
-The **P vs NP** problem can be thought of as a question about pattern recognition. In P, you're given an input and tasked with computing the output efficiently, like running a program. In NP, it’s the reverse: you're given a desired output and need to find the input—or "program"—that produces it.
+The **P vs NP** problem can be thought of as a question about pattern recognition. In P, you're given an input and tasked with computing the output efficiently—in polynomial time. In NP, it’s the reverse: you're given a desired output and need to find the input—or "program"—that produces the output in polynomial time.
 For example, with NP problems like the Boolean satisfiability problem (SAT), verifying if a given solution works is easy (in P), but **finding** that solution is hard, much like trying to reverse-engineer a program to figure out what input created a specific result.
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 Though universal pattern recognition is incomputable, it's possible within finite limits. Perfect pattern recognition works when restricted to a finite set of candidate programs. This means that while AI can solve problems within specific, bounded domains (e.g., diagnosing diseases or navigating traffic), **building better AIs will forever remain open-ended**.
-**The challenge of inverting computation**:
+**The challenge of inverting computation and the general structure of AI algorithms**:
-The **P vs NP** problem is essentially about pattern recognition. In P, computing the output from a given input is easy. In NP, it's much harder: you must reverse the process and find the input (or "program") that generates a specific output. Since **P ≠ NP** is widely believed, it highlights that solving some AI problems—like planning or optimization—may always be more complex than verifying their solutions.
+The **P vs NP** problem fundamentally revolves around the difficulty of pattern recognition. In class **P**, given an input, computing the output is efficient. In class **NP**, however, the challenge is reversed: you need to find the input (or "program") that produces a specific output, a task that is much harder. This highlights a general framework for pattern recognition algorithms: first, analyze the data, then iteratively hypothesize potential programs, verifying at each step whether a given program generates the observed data.
 **AI as a core branch of computer science**:
 AI isn't just an engineering branch about practical problem-solving—it's deeply rooted in computer science theory. Concepts like computation, logic, and complexity are essential for understanding and advancing AI, though their importance is often underplayed. Strengthening these links could unlock new AI breakthroughs by helping researchers better understand the limits and possibilities of computation and pattern recognition. AI's future lies in its deep integration with computer science, focusing more on foundational concepts like algorithmic complexity.