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Algorithm for NP-Complete Sudoku
11 days ago
- The paper proposes a conceptual solution to the P vs NP problem, asserting P = NP under a new structural paradigm.
- It argues the complexity barrier arises from using a deficient algebraic coordinate system (sequential brute force).
- Introducing the NLS Universe (Discrete Equilibrium Structure) claims to collapse combinatorial complexity to constant time O(1).
- A proof-of-concept algorithm for Sudoku (NP-Complete) is presented, illustrating the symmetry of computational effort.
- It posits that solutions are not searched but generated via topological gears and combinatorial parametrization.
Mathematicians still don't know the fastest way to multiply numbers
15 days ago
- The grade-school multiplication algorithm scales with O(n²), requiring more steps as numbers grow.
- Anatoly Karatsuba discovered a faster algorithm in 1960 by reducing multiplications to additions, with a runtime of O(n^1.585).
- Karatsuba's method is used in software like Python for large numbers, typically around 630 decimal digits.
- In 2019, David Harvey and Joris van der Hoeven developed an O(n × log n) algorithm, but it's only practical for 'galactic'-scale numbers.
- Theoretical computer scientists suspect O(n × log n) is the ultimate speed limit, but it remains unproven.
Markets are competitive if and only if P != NP
25 days ago
- The paper argues that competitive markets depend on computational intractability: if P = NP, firms can efficiently detect collusion, making it sustainable; if P ≠ NP, detection is infeasible under certain conditions, preventing collusion stability.
- It links this to Maymin (2011), concluding that markets cannot be both informationally efficient and competitive, forming a fundamental trade-off.
- Artificial intelligence enhances firms' computational power, shifting markets toward collusion and explaining algorithmic collusion without explicit coordination.

Hasty Briefsbeta

computational complexity

Algorithm for NP-Complete Sudoku

Mathematicians still don't know the fastest way to multiply numbers

Markets are competitive if and only if P != NP