A new polynomial-time algorithm for linear programming
Combinatorica
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The complexity of linear problems in fields
Journal of Symbolic Computation
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
Combinatorial theory (2nd ed.)
Combinatorial theory (2nd ed.)
Computer-Aided Reasoning: An Approach
Computer-Aided Reasoning: An Approach
Concrete Mathematics: A Foundation for Computer Science
Concrete Mathematics: A Foundation for Computer Science
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Principles of Constraint Programming
Principles of Constraint Programming
A formally verified proof of the prime number theorem
ACM Transactions on Computational Logic (TOCL)
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
Formal proof of a wave equation resolution scheme: the method error
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Wave Equation Numerical Resolution: A Comprehensive Mechanized Proof of a C Program
Journal of Automated Reasoning
| Hi-index | 0.00 |
Let F be the set of functions from an infinite set, S, to an ordered ring, R. For f, g, and h in F, the assertion f = g + O(h) means that for some constant C, |f(x) 驴 g(x)| 驴C |h(x)| for every x in S. Let L be the first-order language with variables ranging over such functions, symbols for 0, +, 驴, min , max , and absolute value, and a ternary relation f = g + O(h). We show that the set of quantifier-free formulas in this language that are valid in the intended class of interpretations is decidable and does not depend on the underlying set, S, or the ordered ring, R. If R is a subfield of the real numbers, we can add a constant 1 function, as well as multiplication by constants from any computable subfield. We obtain further decidability results for certain situations in which one adds symbols denoting the elements of a fixed sequence of functions of strictly increasing rates of growth.