Automatic 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 are performed automatically, while in some steps human assistance is necessary. Our system (adeptus), which we present in this paper, synthesized a decision procedure for ground arithmetic completely automatically and it used some specific method generators in generating a decision procedure for linear arithmetic. We believe that this approach can lead to automated assistance in constructing decision procedures and to more reliable implementations of decision procedures.