The complexity of elementary algebra and geometry
Journal of Computer and System Sciences
Real quantifier elimination is doubly exponential
Journal of Symbolic Computation
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation
Journal of Symbolic Computation
Efficient solving of quantified inequality constraints over the real numbers
ACM Transactions on Computational Logic (TOCL)
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Causality is one of the most fundamental notions of physics. It is therefore important to be able to decide which statements about causality are correct in different models of space-time. In this paper, we analyze the computational complexity of the corresponding decision problems. In particular, we show that: *for Minkowski space-time, the decision problem is as difficult as Tarski's decision problem for elementary geometry, while *for a natural model of primordial space-time, the corresponding decision problem is of the lowest possible complexity among all possible space-time models.