Complexity of short Presburger arithmetic
Year: 2017
Type: preprint
Abstract: We study complexity of short sentences in Presburger arithmetic (Short-PA). Here by "short" we mean sentences with a bounded number of variables, quantifiers, inequalities and Boolean operations; the input consists only of the integers involved in the inequalities. We prove that assuming Kannan's partition can be found in polynomial time, the satisfiability of Short-PA sentences can be decided in polynomial time. Furthermore, under the same assumption, we show that the numbers of satisfying assignments of short Presburger sentences can also be computed in polynomial time.
Source: arXiv (Cornell University)
Authors: Nguyen, Danny, Pak, Igor
Institution: University of California, Los Angeles
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2958635970