The complexity of linear problems in fields. (English) Zbl 0646.03005

Complexity bounds for decision problems) for linear sentences (that means that in atomic subformulas only linear polynomials occur) over different types of fields are established. It is proved that for fields of zero characteristic or for ordered fields (in the latter case inequalities are allowed) these problems can be solved in exponential space and double exponential time. A similar result is obtained for the discretely valued fields. The decision problem for linear sentences with a fixed number of quantifiers can be solved in polynomial time.
Reviewer: D.Yu.Grigor’ev


03B25 Decidability of theories and sets of sentences
03D15 Complexity of computation (including implicit computational complexity)
12L05 Decidability and field theory
68W30 Symbolic computation and algebraic computation
68Q25 Analysis of algorithms and problem complexity
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