Guarded Monotone Strict NP (GMSNP) extends the class of Monotone Monadic Strict NP (MMSNP) by allowing existentially quantified relations of arities greater than 1 but restricting them to always be guarded by input relations. The containment problem is characterized for MMSNP by the existence of a recoloring which is a mapping between the sets of second-order variables of the two given logical sentences that satisfies some specific properties. This paper extends this characterization to GMSNP problems, where the input signature consists of unary and binary relation symbols.

翻译：有界单调严格NP（GMSNP）通过允许存在量化的关系具有大于1的元数，但限制它们始终由输入关系守卫，从而扩展了单调一元严格NP（MMSNP）类。MMSNP的包含性问题通过重着色的存在性来刻画，该重着色是两个给定逻辑句子的二阶变量集合之间满足某些特定属性的映射。本文将这一刻画扩展到GMSNP问题，其中输入签名由一元和二元关系符号组成。