Arithmetic Decision Procedures: a simple introduction
نویسنده
چکیده
Fourier-Motzkin variable elimination is introduced as a complete method for deciding linear arithmetic inequalities over R. It is then shown how this method can be extended to also work over Z, giving the Omega Test [2].
منابع مشابه
Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making
The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...
متن کاملOnline Proof-Producing Decision Procedure for Mixed-Integer Linear Arithmetic?
Efficient decision procedures for arithmetic play a very important role in formal verification. In practical examples, however, arithmetic constraints are often mixed with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc. Therefore, decision procedures for arithmetic are especially useful in combination with other decision procedures. The...
متن کاملSolving Sparse Linear Constraints
Linear arithmetic decision procedures form an important part of theorem provers for program verification. In most verification benchmarks, the linear arithmetic constraints are dominated by simple difference constraints of the form x ≤ y + c. Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints. In this paper, we propose an eff...
متن کاملAutomatic Synthesis of Decision Procedures: A Case Study of Ground and Linear Arithmetic
In this paper we address the problem of automatic synthesis of decision procedures. We evaluate our ideas on ground arithmetic and Fourier/Motzkin decision procedure for linear arithmetic, but the approach can be applied to other domains as well. The approach is well-suited to the proofplanning paradigm. The synthesis mechanism consists of several stages and sub-mechanisms. Some of these steps ...
متن کاملA Practical Extension Mechanism for Decision Procedures: the Case Study of Universal Presburger Arithmetic
In this paper, we propose a generic mechanism for extending decision procedures by means of a lemma speculation mechanism. This problem is important in order to widen the scope of decision procedures incorporated in state-of-the-art veri cation systems. Soundness and termination of the extension schema are formally stated and proved. As a case study, we consider extensions of a decision procedu...
متن کامل