Applications Because Presburger arithmetic is decidable, automatic theorem provers for Presburger arithmetic exist. Source: Internet
For example, the Coq proof assistant system features the tactic omega for Presburger arithmetic and the Isabelle proof assistant contains a verified quantifier elimination procedure by Nipkow (2010). Source: Internet
Examples include finding a perfect strategy for chess (on an N × N board) citation and some other board games. citation The problem of deciding the truth of a statement in Presburger arithmetic requires even more time. Source: Internet
Fischer and Rabin's work also implies that Presburger arithmetic can be used to define formulas which correctly calculate any algorithm as long as the inputs are less than relatively large bounds. Source: Internet
For example, the decision problem in Presburger arithmetic has been shown not to be in P, yet algorithms have been written that solve the problem in reasonable times in most cases. Source: Internet
Generally, any number concept leading to multiplication cannot be defined in Presburger arithmetic, since that leads to incompleteness and undecidability. Source: Internet