2022/01/14 by George Barmpalias, Lu Liu, Barmpalias, George +1
Computer Science · #Computability, Logic, AI Algorithms #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2201.07007
openalex publication_date 2022/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Muchnik's paradox says that enumerable betting strategies are not always reducible to enumerable strategies whose bets are restricted to either even rounds or odd rounds. In other words, there are outcome sequences x where an effectively enumerable strategy succeeds, but no such parity-restricted effectively enumerable strategy does. We characterize the effective Hausdorff dimension of such x, showing that it can be as low as 1/2 but not less. We also show that such reals that are random with respect to parity-restricted effectively enumerable strategies with packing dimension as low as log√3. Finally we exhibit Muchnik's paradox in the case of computable integer-valued strategies.