# ASNP: a tame fragment of existential second-order logic

From International Center for Computational Logic

# ASNP: a tame fragment of existential second-order logic

*Talk by Manuel Bodirsky and Simon Knäuer*

- Location: Digital
- Start: 25. June 2020 at 1:00 pm
- End: 25. June 2020 at 2:30 pm
- Event series: KBS Seminar
- iCal

Amalgamation SNP (ASNP) is a fragment of existential second-order logic that strictly contains binary connected MMSNP of Feder and Vardi and binary connected 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.

This will be a test talk for the presentation of an eponymous paper consisting of the 20 minute long prerecorded talk (like it will be presented at the conference) which will be followed up with a Q&A session to the talk where questions will be answered by Simon Knäuer, one of the authors. Feedback and suggestions in preperation for the conference talk are heavily encouraged.