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Many theorems involving special functions such as ln, exp and sin can be proved automatically by MetiTarski: a resolution theorem prover modified to call a decision procedure for the theory of real closed fields. Special functions are approximated by upper and lower bounds, which are typically rational functions derived from Taylor or continued fraction… (More)

—MetiTarski, an automatic theorem prover for inequalities on real-valued elementary functions, can be used to verify properties of analog circuits. First, a closed form solution to the model of the circuit is obtained. We present two techniques for obtaining the closed form solution. One is based on piecewise linear modeling and the inverse Laplace… (More)

MetiTarski, an automatic proof procedure for inequalities on elementary functions, can be used to verify control and hybrid systems. We perform a stability analysis of control systems using Nichols plots, presenting an inverted pendulum and a magnetic disk drive reader system. Given a hybrid systems specified by a system of differential equations , we use… (More)

Expectation (average) properties of continuous random variables are widely used to judge performance characteristics in engineering and physical sciences. This paper presents an infrastructure that can be used to formally reason about expectation properties of most of the continuous random variables in a theorem prover. Starting from the relatively complex… (More)

Many inequalities involving the functions ln, exp, sin, cos, etc., can be proved automatically by MetiTarski: a resolution theorem prover (Metis) modified to call a decision procedure (QEPCAD) for the theory of real closed fields. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts, while deleting… (More)

Inequalities involving functions such as sines, exponentials and logarithms lie outside the scope of decision procedures, and can only be solved using heuristic methods. Preliminary investigations suggest that many such problems can be solved by reduction to algebraic inequalities, which can then be decided by a decision procedure for the theory of real… (More)

Experiments show that many inequalities involving exponen-tials and logarithms can be proved automatically by combining a resolution theorem prover with a decision procedure for the theory of real closed fields (RCF). The method should be applicable to any functions for which polynomial upper and lower bounds are known. Most bounds only hold for specific… (More)