Termination of one-variable linear-constraint loops over integers is decidable in polynomial time if the generalized Collatz conjecture holds, with any such procedure also settling specific instances of the conjecture.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
years
2026 2verdicts
UNVERDICTED 2representative citing papers
New FPT algorithms solve standard-form ILP optimization in O(κ_k)^{2k} Δ² time and feasibility in O(κ_k)^k Δ time, where κ_k is the Komlós discrepancy constant, giving polylog(k) factors with known bounds and 2^{O(k)} under the conjecture.
citing papers explorer
-
Loop Termination and Generalized Collatz Sequences
Termination of one-variable linear-constraint loops over integers is decidable in polynomial time if the generalized Collatz conjecture holds, with any such procedure also settling specific instances of the conjecture.
-
Algorithms for Standard-form ILP Problems via Koml\'os' Discrepancy Setting
New FPT algorithms solve standard-form ILP optimization in O(κ_k)^{2k} Δ² time and feasibility in O(κ_k)^k Δ time, where κ_k is the Komlós discrepancy constant, giving polylog(k) factors with known bounds and 2^{O(k)} under the conjecture.