Static Symmetry Breaking in Many-Sorted Finite Model Finding

Abstract: Symmetry in finite model finding problems of many-sorted first-order logic (MSFOL) can be exploited to reduce the number of interpretations considered during search, thereby improving solver performance. In this thesis, we situate symmetry of many-sorted finite model finding (MSFMF) problems in a general framework used for constraint satisfaction problems (CSP). We survey and classify existing approaches to symmetry for MSFOL as used in tools such as Paradox. We provide new insight into how sorts affect the existence of symmetry and how sort inference can be viewed as a symmetry detection mechanism. Finally, we present two new symmetry breaking schemes for MSFOL that are implemented at the MSFOL level and discuss when schemes can be combined. We prove the correctness of our new methods.