Deciding linear-trigonometric problems

In this paper, we present a decision procedure for certain linear-trigonometric problems for the reals and integers formalized in a suitable first-order language. The inputs are restricted to formulas, where all but one of the quantified variables occur linearly and at most one occurs both linearly and in a specific trigonometric function. Moreover we may allow in addition the integer-part operation in formulas. Besides ordinary quantifiers, we allow also counting quantifiers. Furthermore we also determine the qualitative structure of the connected components of the satisfaction set of the mixed linear-trigonometric variable. We also consider the decision of these problems in subfields of the real algebraic numbers.

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