Amalgamation SNP (ASNP) is a fragment of existential second-order logic that strictly contains binary connected MMSNP of Feder and Vardi and binary guarded monotone SNP of Bienvenu, ten Cate, Lutz, and Wolter; it is a promising candidate for an expressive subclass of NP that exhibits a complexity dichotomy. We show that ASNP has a complexity dichotomy if and only if the infinite-domain dichotomy conjecture holds for constraint satisfaction problems for first-order reducts of binary finitely bounded homogeneous structures. For such CSPs, powerful universal-algebraic hardness conditions are known that are conjectured to describe the border between NP-hard and polynomial-time tractable CSPs. The connection to CSPs also implies that every ASNP sentence can be evaluated in polynomial time on classes of finite structures of bounded treewidth. We show that the syntax of ASNP is decidable. The proof relies on the fact that for classes of finite binary structures given by finitely many forbidden substructures, the amalgamation property is decidable.

中文翻译：

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ASNP：存在二阶逻辑的驯服片段

Amalgamation SNP (ASNP) 是存在性二阶逻辑的一个片段，它严格包含 Feder 和 Vardi 的二元连通 MMSNP 和 Bienvenu、十 Cate、Lutz 和 Wolter 的二元保护单调 SNP；它是表现复杂性二分法的 NP 的表达子类的一个有希望的候选者。我们表明，当且仅当无限域二分法猜想适用于二元有限有界齐次结构的一阶约简的约束满足问题时，ASNP 具有复杂性二分法。对于此类 CSP，已知强大的通用代数硬度条件可以用来描述 NP 难和多项式时间易处理 CSP 之间的边界。与 CSP 的联系还意味着每个 ASNP 句子都可以在多项式时间内对有界树宽的有限结构类进行评估。我们证明了 ASNP 的语法是可判定的。证明依赖于以下事实：对于由有限多个禁止子结构给出的有限二元结构类，合并属性是可判定的。