Melvin's digital garden

Complexity of integer division

CREATED: 200710120221

Paul W. Beame, Stephen A. Cook, and H. James Hoover. Log depth circuits for division and related problems

  • integer divisibility is in L

Andrew Chiu, George Davida, and Bruce Litow. Division in logspace-uniform NC1

  • integer division is in L

Uniform constant-depth threshold circuits for division and iterated multiplication

  • integer division is in DLOGTIME-uniform TC0

Eric Allender. The Division Breakthroughs

  • survey of the recents from the previous three

Q: Why is the classical binary long division not in L?

A: L computable means using O(log n) working memory where n is the number of bits. Assume input is given read-only and output is write-only and doesn’t count towards working memory.

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