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Computing the Homology of Semialgebraic Sets. II: General Formulas

机译：Computing the Homology of Semialgebraic Sets. II: General Formulas

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Abstract We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially small measure, the cost of the algorithm is single exponential in the size of the data. This extends the work in Part?I to arbitrary semialgebraic sets. All previous algorithms proposed for this problem have doubly exponential complexity.

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