Abstract. Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. This can be important, with some problems infeasible with one variable ordering but easy with another. Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data. In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.

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Case splitting, with and without backtracking, is compared with straightforward ordered resolution. Both forms of splitting have been implemented for MetiTarski, an automatic theorem prover for real-valued special functions such as exp, ln, sin, cos and tan −1 . The experimental findings confirm the superiority of true backtracking over the simulation of backtracking through the introduction of new predicate symbols, and the superiority of both over straightforward resolution.

Abstract. We explore uses of a link we have constructed between the KeYmaera hybrid systems theorem prover and the MetiTarski proof engine for problems involving special functions such as sin, cos, exp, etc. Transcendental functions arise in the specification of hybrid systems and often occur in the solutions of the differential equations that govern how the states of hybrid systems evolve over time. To date, formulas exchanged between KeYmaera and external tools have involved polynomials over the reals, but not transcendental functions, chiefly because of the lack of tools capable of proving such goals.

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