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Characterizing Streaming Decidability of CSPs via Non-Redundancy

Authors Amatya Sharma , Santhoshini Velusamy

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ACM Subject Classification
  • Theory of computation → Streaming models
  • Theory of computation → Lower bounds and information complexity
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Constraint Satisfaction Problems
  • Streaming Algorithms
  • Satisfiability
  • Non-Redundancy

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Abstract

We study the single-pass streaming complexity of deciding satisfiability of Constraint Satisfaction Problems (CSPs). A CSP is specified by a constraint language Γ, that is, a finite set of k-ary relations over the domain [q] = {0, … , q-1}. An instance of CSP(Γ) consists of m constraints over n variables x₁, …, x_n taking values in [q]. Each constraint C_i is of the form {R_i,(x_{i_1} + λ_{i_1}, …, x_{i_k} + λ_{i_k})}, where R_i ∈ Γ and λ_{i_1}, …, λ_{i_k} ∈ [q] are constants; it is satisfied if and only if (x_{i_1} + λ_{i_1}, …, x_{i_k} + λ_{i_k}) ∈ R_i, where addition is modulo q. In the streaming model, constraints arrive one by one, and the goal is to determine, using minimum memory, whether there exists an assignment satisfying all constraints.
For k-SAT, Vu (TCS 2024) proves an optimal Ω_k(n^k) space lower bound, while for general CSPs, Chou, Golovnev, Sudan, and Velusamy (JACM 2024) establish an Ω(n) lower bound; a complete characterization has remained open. We close this gap by showing that the single-pass streaming space complexity of CSP(Γ) is precisely governed by its non-redundancy, a structural parameter introduced by Bessiere, Carbonnel, and Katsirelos (AAAI 2020). The non-redundancy NRD_n(Γ) is the maximum number of constraints over n variables such that every constraint is non-redundant, i.e., omitting it strictly expands the set of satisfying assignments. We prove that the single-pass streaming complexity of CSP(Γ) is characterized, up to a logarithmic factor, by NRD_n(Γ). We also extend this characterization to positive Boolean CSPs, i.e., instances in which no additive shifts are applied, a class that includes graph 2-colorability (equivalently, bipartiteness) as a canonical example.
A key ingredient in our lower bound proof is a binary relation ℰ on the set of assignments [q]ⁿ, where (a, b) ∈ ℰ if every instance satisfied by a is also satisfied by b. While it is immediate that ℰ is reflexive and transitive, its symmetry, which would make it an equivalence relation, is non-trivial. We show that ℰ is an equivalence relation for general CSPs, and for positive Boolean CSPs when excluding the two constant assignments (0ⁿ and 1ⁿ). We believe this equivalence structure could be of independent interest.

Cite As Get BibTex

Amatya Sharma and Santhoshini Velusamy. Characterizing Streaming Decidability of CSPs via Non-Redundancy. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 131:1-131:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.131

Author Details

Amatya Sharma
  • University of Michigan, Ann Arbor, MI, USA
Santhoshini Velusamy
  • University of Waterloo, Canada

Funding

  • Sharma, Amatya: Work done in part when the author was visiting the Toyota Technological Institute at Chicago as an intern in Fall 2025.
  • Velusamy, Santhoshini: Supported by NSERC Discovery grant RGPIN-2026-04689 and ECR supplement DGECR-2026-00421. Supported in part by NSF award CCF 2348475 when the author was affiliated with Toyota Technological Institute at Chicago.

Acknowledgements

We thank Joshua Brakensiek, Aaron Putterman, and Venkatesan Guruswami for helping us better understand the context of NRD in the literature. We also thank the anonymous reviewers of ESA 2026 for their helpful feedback.

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