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）通过允许存在量词约束的元数大于1的关系，但限制其始终受到输入关系的约束，从而扩展了单调一元严格NP（MMSNP）类。MMSNP的包含性问题可通过重着色（recoloring）的存在性来刻画，该重着色是两个给定逻辑语句的二阶变量集之间满足特定性质的映射。本文将此刻画扩展至输入签名包含一元和二元关系符号的GMSNP问题。