Temporal Constraint Satisfaction Problems in Fixed-Point Logic

Bodirsky, Manuel; Pakusa, Wied; Rydval, Jakub

doi:10.1145/3373718.3394750

Cited by 10 publications

(8 citation statements)

References 25 publications

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“…We also showed that every CSP in GSO can be formulated as a CSP of an ω-categorical structure. These results also imply that the so-called universal-algebraic approach, which has eventually led to the classification of finite-domain CSPs in Datalog [3], can be applied to study problems that are simultaneously in Datalog and in GSO (also see [9]). Our results might also pave the way towards a syntactic characterisation of Datalog ∩ GSO.…”

Section: Conclusion and Open Problemsmentioning

confidence: 87%

Datalog-Expressibility for Monadic and Guarded Second-Order Logic

Bodirsky¹,

Knäuer²,

Rudolph³

2020

Preprint

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We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be expressed in MSO and is closed under homomorphisms, and for all , k ∈ N, there exists a canonical Datalog program Π of width ( , k), that is, a Datalog program of width ( , k) which is sound for C (i.e., Π only derives the goal predicate on a finite structure A if A ∈ C) and with the property that Π derives the goal predicate whenever some Datalog program of width ( , k) which is sound for C derives the goal predicate. The same characterisations also hold for Guarded Second-order Logic (GSO), which properly extends MSO. To prove our results, we show that every class C in GSO whose complement is closed under homomorphisms is a finite union of constraint satisfaction problems (CSPs) of ω-categorical structures.

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Section: Conclusion and Open Problemsmentioning

confidence: 87%

Datalog-Expressibility for Monadic and Guarded Second-Order Logic

Bodirsky¹,

Knäuer²,

Rudolph³

2020

Preprint

Self Cite

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“…An algebraic characterisation of local consistency checking for infinite-domain CSPs is, however, missing. In fact, the negative results of [18], refined in [34], show that no purely algebraic description of local consistency is possible for CSPs with ω-categorical templates; this is even the case for temporal CSPs [19]. These negative results are to be compared with the recent result by Mottet and Pinsker [42] that did provide an algebraic description of local consistency for several subclasses of ω-categorical templates.…”

Section: Introductionmentioning

confidence: 82%

“…In the latter case we are done by Theorem 1.2, in the former we appeal to the syntactical characterization of first-order reducts of (Q, <). Indeed, such a structure has bounded width iff it is definable by a conjunction of so-called Ord-Horn clauses [19]. It then follows by [27] that a first-order reduct of (Q; <) with bounded width has relational width (2,3).…”

Section: Introductionmentioning

confidence: 99%

When symmetries are enough: collapsing the bounded width hierarchy for infinite-domain CSPs

Mottet¹,

Nagy²,

Pinsker³

et al. 2021

Preprint

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We prove that relational structures admitting specific polymorphisms (namely, canonical pseudo-WNU operations of all arities n ≥ 3) have low relational width. This implies a collapse of the bounded width hierarchy for numerous classes of infinite-domain CSPs studied in the literature. Moreover, we obtain a characterization of bounded width for first-order reducts of unary structures and a characterization of MMSNP sentences that are equivalent to a Datalog program, answering a question posed by Bienvenu et al.. In particular, the bounded width hierarchy collapses in those cases as well.

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“…Can we decide algorithmically whether a given ASNP sentence is equivalent (over finite structures) to a fixed-point logic sentence (this then implies that the problem is in P)? We refer to [9] for a recent article on the power of fixed-point logic for infinite-domain CSPs. 4.…”

Section: Is the Amalgamation Property Decidable For (Not Necessarily ...mentioning

confidence: 99%

ASNP: a tame fragment of existential second-order logic

Bodirsky¹,

Knäuer²,

Starke³

2020

Preprint

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Amalgamation SNP (ASNP) is a fragment of existential secondorder 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.

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Temporal Constraint Satisfaction Problems in Fixed-Point Logic

Cited by 10 publications

References 25 publications

Datalog-Expressibility for Monadic and Guarded Second-Order Logic

Datalog-Expressibility for Monadic and Guarded Second-Order Logic

When symmetries are enough: collapsing the bounded width hierarchy for infinite-domain CSPs

ASNP: a tame fragment of existential second-order logic

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