The Complexity of Combinations of Qualitative Constraint Satisfaction Problems

Bodirsky, Manuel; Greiner, Johannes

doi:10.23638/lmcs-16(1:21)2020

Cited by 1 publication

(4 citation statements)

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“…Generic Combinations. In the context of combining decision procedures for CSPs, the notion of generic combinations has been introduced in [BG20]. However, others have studied such structures before (for instance in [Cam90, KPT05, BPP15, LP15]).…”

Section: The Conditions Ofmentioning

confidence: 99%

“…All generic combinations of A 1 and A 2 are isomorphic (Lemma 2.8 in [BG20]), so we will speak of the generic combination of two structures, and denote it by…”

Section: The Conditions Ofmentioning

confidence: 99%

“…Theorem 2.5 Proposition 1.1 in [BG20]. Let A 1 and A 2 be countably infinite ω-categorical structures with disjoint relational signatures.…”

Section: The Conditions Ofmentioning

confidence: 99%

“…, b n ), because both (Q; <) and A do not have algebraicity. Now we apply the first statement of Lemma 2.7 in [BG20] for each k ∈ [n] to c, s k,1 , s k,2 . This yields, for each k ∈ [n], a solution s k to ψ k ∧ φ(x k , y k , u k , v k ).…”

Section: Temporal Structuresmentioning

confidence: 99%

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Tractable Combinations of Temporal CSPs

Bodirsky¹,

Greiner²,

Rydval³

2022

Logical Methods in Computer Science

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The constraint satisfaction problem (CSP) of a first-order theory T is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of T. We study the computational complexity of CSP$(T_1 \cup T_2)$ where $T_1$ and $T_2$ are theories with disjoint finite relational signatures. We prove that if $T_1$ and $T_2$ are the theories of temporal structures, i.e., structures where all relations have a first-order definition in $(Q;<)$, then CSP$(T_1 \cup T_2)$ is in P or NP-complete. To this end we prove a purely algebraic statement about the structure of the lattice of locally closed clones over the domain $Q$ that contain Aut$(Q;<)$.

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Section: The Conditions Ofmentioning

confidence: 99%

“…All generic combinations of A 1 and A 2 are isomorphic (Lemma 2.8 in [BG20]), so we will speak of the generic combination of two structures, and denote it by…”

Section: The Conditions Ofmentioning

confidence: 99%

“…Theorem 2.5 Proposition 1.1 in [BG20]. Let A 1 and A 2 be countably infinite ω-categorical structures with disjoint relational signatures.…”

Section: The Conditions Ofmentioning

confidence: 99%

Section: Temporal Structuresmentioning

confidence: 99%

See 2 more Smart Citations