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 expansions. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts. MetiTarski simplifies arithmetic expressions by conversion to a recursive representation, followed by flattening of nested quotients. Applications include verifying hybrid and control systems.

Abstract. Experiments show that many inequalities involving exponentials 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 argument ranges, but resolution can automatically perform the necessary case analyses. The system consists of a superposition prover (Metis) combined with John Harrison's RCF solver and a small amount of code to simplify literals with respect to the RCF theory.

Abstract. 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 Maple to obtain a problem involving the exponential and trigonometric functions, which MetiTarski can prove automatically.

Abstract. 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 as redundant clauses that follow algebraically from other clauses. MetiTarski includes special code to simplify arithmetic expressions.

Deep datapath and algorithm complexity have made the verification of floating-point units a very hard task. Most simulation and reachability analysis verification tools fail to verify a circuit with a deep datapath like most industrial floating-point units. Theorem proving, however, offers a better solution to handle such verification. In this paper, we have hierarchically formalized and verified a hardware implementation of the IEEE-754 table-driven floating-point exponential function algorithm using the HOL theorem prover. The high ability of abstraction in the HOL verification system allows its use for the verification task over the whole design path of the circuit, starting from gate level implementation of the circuit up to a high level mathematical specification.