On the Satisfiability of Modular Arithmetic Formula
نویسنده
چکیده
Modular arithmetic is the underlying integer computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of modular arithmetic formulae over the finite ring Z2ω . Although an upper bound of 2 2 4) can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Further, we give an efficient reduction to integer programming with the number of constraints and variables linear in the length of the given linear modular arithmetic formula. For non-linear modular arithmetic formulae, an additional factor of ω is needed. With the advent of efficient integer programming packages, our word-level encoding could be useful to software verification in practice.
منابع مشابه
On the Satisfiability of Modular Arithmetic Formulae
Modular arithmetic is the underlying integral computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of propositional formulae in modular arithmetic over the finite ring Z2ω . Although an upper bound of 2 2 O(n4) can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Fur...
متن کاملSMT Beyond DPLL(T): A New Approach to Theory Solvers and Theory Combination
Satisifiability modulo theories (smt) is the problem of deciding whether a given logical formula can be satisifed with respect to a combination of background theories. The past few decades have seen many significant developments in the field, including fast Boolean satisfiability solvers (sat), efficient decision procedures for a growing number of expressive theories, and frameworks for modular...
متن کاملArithmetic Intersection on a Hilbert Modular Surface and the Faltings Height
In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over Z. As applications, we obtain the first ‘non-abelian’ Chowla-Selberg formula, which is a special case of Colmez’s conjecture; an explicit arithmetic intersection formula between arithmetic Humbert surfaces and CM cycles in t...
متن کاملOn Intervals and Bounds in Bit-vector Arithmetic
Bit-vector arithmetic operations rely on modular arithmetic semantics, which often complicates algebraic manipulations. One such example are inequalities. Satisfiability of a system of modular inequalities is NP-complete [1]. In this memo we investigate a simple type of inequalities: only one variable is permitted and there are no multiplications. Satisfiability is solved in polynomial time by ...
متن کاملAn arithmetic intersection formula on Hilbert modular surfaces
In this paper, we obtain an explicit arithmetic intersection formula on a Hilbert modular surface between the diagonal embedding of the modular curve and a CM cycle associated to a nonbiquadratic CM quartic field. This confirms a special case of the author’s conjecture with J. Bruinier, and is a generalization of the beautiful factorization formula of Gross and Zagier on singular moduli. As an ...
متن کامل