# Fast counting with tensor networks

## Abstract

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

- Authors:

- Boston University
- University of Central Florida

- Publication Date:

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1574034

- Grant/Contract Number:
- FG02-06ER46316

- Resource Type:
- Published Article

- Journal Name:
- SciPost Physics Proceedings

- Additional Journal Information:
- Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 5; Journal ID: ISSN 2542-4653

- Publisher:
- Stichting SciPost

- Country of Publication:
- Netherlands

- Language:
- English

### Citation Formats

```
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, and Ruckenstein, Andrei. Fast counting with tensor networks. Netherlands: N. p., 2019.
Web. doi:10.21468/SciPostPhys.7.5.060.
```

```
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, & Ruckenstein, Andrei. Fast counting with tensor networks. Netherlands. doi:10.21468/SciPostPhys.7.5.060.
```

```
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, and Ruckenstein, Andrei. Tue .
"Fast counting with tensor networks". Netherlands. doi:10.21468/SciPostPhys.7.5.060.
```

```
@article{osti_1574034,
```

title = {Fast counting with tensor networks},

author = {Kourtis, Stefanos and Chamon, Claudio and Mucciolo, Eduardo and Ruckenstein, Andrei},

abstractNote = {We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.},

doi = {10.21468/SciPostPhys.7.5.060},

journal = {SciPost Physics Proceedings},

number = 5,

volume = 7,

place = {Netherlands},

year = {2019},

month = {11}

}

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DOI: 10.21468/SciPostPhys.7.5.060

DOI: 10.21468/SciPostPhys.7.5.060

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