Incremental SAT solving under assumptions, introduced in Minisat, is in wide use. However, Minisat’s algorithm for incremental SAT solving under assumptions has two main drawbacks which hinder performance considerably. First, it is not compliant with the highly effective and commonly used preprocessor SatELite. Second, all the assumptions are left in the formula, rather than being represented a...

We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in K-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms ar...

We introduce the notion of ultimately bipartite impartial games. These are games that are ultimately periodic in the simplest possible manner. We examine ultimately bipartite subtraction games and demonstrate a curious feature: for ‘large’ games it is clear who has the winning position and how the game should be strategically played, but during play, as the game eventually becomes small, it is ...