Characterizing Streaming Decidability of CSPs via Non-Redundancy
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| Format: | Preprint |
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2026
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| _version_ | 1866914563608281088 |
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| author | Sharma, Amatya Velusamy, Santhoshini |
| author_facet | Sharma, Amatya Velusamy, Santhoshini |
| contents | 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 $[q] = \{0, \dots, q-1\}$. An instance of $\mathsf{CSP}(Γ)$ consists of $m$ constraints over $n$ variables $x_1, \ldots, x_n$ taking values in $[q]$. Each constraint $C_i$ is of the form $\{R_i,(x_{i_1} + λ_{i_1}, \ldots, x_{i_k} + λ_{i_k})\}$, where $R_i \in Γ$ and $λ_{i_1}, \ldots, λ_{i_k} \in [q]$ are constants; it is satisfied if and only if $(x_{i_1} + λ_{i_1}, \ldots, x_{i_k} + λ_{i_k}) \in R_i$, 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 $Ω(n^k)$ 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 $\mathsf{CSP}(Γ)$ is precisely governed by its non-redundancy, a structural parameter introduced by Bessiere, Carbonnel, and Katsirelos (AAAI 2020). The non-redundancy $\mathsf{NRD}_n(Γ)$ is the maximum number of constraints over $n$ variables such that every constraint $C$ is non-redundant, i.e., there exists an assignment satisfying all constraints except $C$. We prove that the single-pass streaming complexity of $\mathsf{CSP}(Γ)$ is characterized, up to a logarithmic factor, by $\mathsf{NRD}_n(Γ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizing Streaming Decidability of CSPs via Non-Redundancy Sharma, Amatya Velusamy, Santhoshini Data Structures and Algorithms Computational Complexity 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 $[q] = \{0, \dots, q-1\}$. An instance of $\mathsf{CSP}(Γ)$ consists of $m$ constraints over $n$ variables $x_1, \ldots, x_n$ taking values in $[q]$. Each constraint $C_i$ is of the form $\{R_i,(x_{i_1} + λ_{i_1}, \ldots, x_{i_k} + λ_{i_k})\}$, where $R_i \in Γ$ and $λ_{i_1}, \ldots, λ_{i_k} \in [q]$ are constants; it is satisfied if and only if $(x_{i_1} + λ_{i_1}, \ldots, x_{i_k} + λ_{i_k}) \in R_i$, 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 $Ω(n^k)$ 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 $\mathsf{CSP}(Γ)$ is precisely governed by its non-redundancy, a structural parameter introduced by Bessiere, Carbonnel, and Katsirelos (AAAI 2020). The non-redundancy $\mathsf{NRD}_n(Γ)$ is the maximum number of constraints over $n$ variables such that every constraint $C$ is non-redundant, i.e., there exists an assignment satisfying all constraints except $C$. We prove that the single-pass streaming complexity of $\mathsf{CSP}(Γ)$ is characterized, up to a logarithmic factor, by $\mathsf{NRD}_n(Γ)$. |
| title | Characterizing Streaming Decidability of CSPs via Non-Redundancy |
| topic | Data Structures and Algorithms Computational Complexity |
| url | https://arxiv.org/abs/2604.21922 |