System for automatic generation of logical formulas

¹ AGH University of Science and Technology, Department of Computer Science, Al. Mickiewicza 30, 30-059 Kraków
² AGH University of Science and Technology, Department of Automatics and Robotics, Al. Mickiewicza 30, 30-059 Kraków

^* Corresponding author: rklimek@agh.edu.pl

Abstract

The satisfiability problem (SAT) is one of the classical and also most important problems of the theoretical computer science and has a direct bearing on numerous practical cases. It is one of the most prominent problems in artificial intelligence and has important applications in many fields, such as hardware and software verification, test-case generation, AI planning, scheduling, and data structures that allow efficient implementation of search space pruning. In recent years, there has been a huge development in SAT solvers, especially CDCL-based solvers (Conflict-Driven Clause-Learning) for propositional logic formulas. The goal of this paper is to design and implement a simple but effective system for random generation of long and complex logical formulas with a variety of difficulties encoded inside. The resulting logical formulas, i.e. problem instances, could be used for testing existing SAT solvers. The entire system would be widely available as a web application in the client-server architecture. The proposed system enables generation of syntactically correct logical formulas with a random structure, encoded in a manner understandable to SAT Solvers. Logical formulas can be presented in different formats. A number of parameters affect the form of generated instances, their complexity and physical dimensions. The randomness factor can be entered to every generated formula. The developed application is easy to modify and open for further extensions. The final part of the paper describes examples of solvers’ tests of logical formulas generated by the implemented generator.