Is Bit-Vector Reasoning as Hard as NExpTime in Practice?

It has been shown that (quantifier-free) bit-vector logic (BV) is NExpTime-complete, on account of the fact that the number of propositional variables in the SAT encoding of a BV formula grows exponentially with the length of the declarations of the bit-vector variables in the input formula. This level of complexity is surprising, given that in practice BV is being used successfully in a wide range of applications. This work points out that the high complexity does not necessary hold in practical applications of BV. We give two examples of easier families of BV problems. First, we demonstrarate that in a BV subset, originating in a recent critical Intel application of BV from clock routing, the number of propositional variables is polynomial in the size of the BV instance – since the maximal value of the instance’s bit-vector variables is written out explicitly as a bit-vector constant, thus establishing that clock routing uses an NP-complete subset of BV. Second, we show that for another application, namely, microcode validation, the (logarithm of the) register width should be viewed as a fixed parameter, and thus microcode validation uses a paraNP-complete parameterized version of BV. Similar arguments are likely to apply to a variety of other BV applications to demonstrate that they too use NP-complete subclasses of BV or its para-NP-complete parametrized version.