Methods and systems for verifying a hardware design for an integrated circuit that implements a function that is polynomial in an input variable x over a set of values of x. The method includes formally verifying that a first instantiation of the hardware design implements a function that is polynomial of degree k in x by formally verifying that for all x in the set of values of x the first instantiation of the hardware design has a constant k.sup.th difference; and verifying that a second instantiation of the hardware design generates an expected output in response to each of at least k different values of x in the set of values of x.

Methods and systems for verifying a property of an integrated circuit hardware design. The method includes formally verifying, using a formal verification tool, that the property is true for the hardware design under a constraint that an instantiation of the hardware design transitions to a quiescent state at a symbolic time.

Methods and systems for verifying a hardware design for an integrated circuit that implements a function that is polynomial of degree k in a sub-function p over a set of values of p, k being an integer greater than or equal to one. The methods include: verifying that an instantiation of the hardware design correctly evaluates the sub-function p; formally verifying that an instantiation of the hardware design implements a function that is polynomial of degree k in p by formally verifying that, for all values of p in the set of values of p, an instantiation of the hardware design has a constant k.sup.th difference; and verifying that an instantiation of the hardware design generates an expected output in response to each of at least e different values of p in the set of values of p, wherein e is equal to k when a value of the k.sup.th difference is predetermined and e is equal to k+1 when the value of the k.sup.th difference is not predetermined.

Methods and systems for verifying a hardware design for an integrated circuit that implements a function that is polynomial in an input variable x over a set of values of x. The method includes formally verifying that a first instantiation of the hardware design implements a function that is polynomial of degree k in x by formally verifying that for all x in the set of values of x the first instantiation of the hardware design has a constant k.sup.th difference; and verifying that a second instantiation of the hardware design generates an expected output in response to each of at least k different values of x in the set of values of x.