Encoding Basic Arithmetic Operations for SAT-Solvers
نویسندگان
چکیده
In this paper we start an investigation to check the best we can do with SAT encodings for solving two important hard arithmetic problems, integer factorization and discrete logarithm. Given the current success of using SAT encodings for solving problems with linear arithmetic constraints, studying the suitability of SAT for solving non-linear arithmetic problems was a natural step. However, our results indicate that these two problems are extremely hard for state-of-the-art SAT solvers, so they are good benchmarks for the research community interested in finding good SAT encodings for practical constraints.
منابع مشابه
The Effects of Arithmetic Encodings on SAT Solver Performance
As digital systems continue to grow, verification of these systems is becoming an increasingly important and difficult problem. To ensure a quick time-to-market, the verification problem must be addressed early in the design cycle. This requires the ability to verify systemlevel descriptions of hardware and embedded software systems, such as, C or Verilog, by proving assertions and proving func...
متن کاملSWORD - Module-based SAT Solving
In this paper, we describe SWORD – a decision procedure for bit-vector logic that uses SAT techniques and exploits word level information [6]. The main idea of SWORD is based on the following observation: While current SAT solvers perform very well on instances with a large number of logic operations, their performance on arithmetic operations degrades with increasing data-path width. In contra...
متن کاملSWORD v0.2 – Module-based SAT Solving
In this paper, we present SWORD – a SAT like solver that facilitates word level information. The main idea behind SWORD is based on the following observation: Current SAT solvers perform very well on instances with a large number of logic operations. But when more complex functions like arithmetic units are considered, the performance degrades with increasing data-path width. In contrast, pure ...
متن کاملA Compact and Efficient SAT-Encoding of Finite Domain CSP
Extended Abstract A (finite) Constraint Satisfaction Problem (CSP) is a combinatorial problem to find an assignment which satisfies all given constraints over finite domains. A SAT-based CSP solver is a program which solves a CSP by encoding it to SAT and searching solutions by SAT solvers. Remarkable improvements in the efficiency of SAT solvers make SAT-based CSP solvers applicable for solvin...
متن کاملA Tutorial on Satisfiability Modulo Theories
Solvers for satisfiability modulo theories (SMT) check the satisfiability of first-order formulas containing operations from various theories such as the Booleans, bit-vectors, arithmetic, arrays, and recursive datatypes. SMT solvers are extensions of Boolean satisfiability solvers (SAT solvers) that check the satisfiability of formulas built from Boolean variables and operations. SMT solvers h...
متن کامل