arXiv subjects

Jincheng Guan

Publications and source records attributed to Jincheng Guan.

3 recordsLinked to original sources

arXiv2026

A Dichotomy for Boolean Complex Holant Problems with Conjugate-Closed Signature Sets

We study Boolean Holant problems with complex-valued signature sets closed under conjugation. Such sets arise naturally in tensor-network expressions for classical strong simulation of quantum circuits. We prove a complexity dichotomy for such problems with an explicit tractability criterion. This extends the dichotomy for real-valued Holant problems, with the same four tractability conditions. Our proofs use Xia's projective binary group framework and quantum entanglement theory. The conjugate closure assumption precisely makes $k$-uniformity, directly applicable to the classification of Holant problems, by realizing reduced density matrices via Holant gadgets. We also use the classification of absolutely maximally entangled states to resolve a particular $6$-ary obstruction in our inductive proof of the \#P-hardness.

cs.CC↗

arXiv2026

An LP Algorithm for Counting Eulerian Orientations Through the Lens of Quasi-polymorphism

The weighted Eulerian orientation counting problem ($\#\mathrm{EO}$) plays a key role in the complexity classification program for Holant problems. A recent result established an $\mathrm{FP}^{\mathrm{NP}}$ versus $\#\mathrm{P}$-hard dichotomy for $\#\mathrm{EO}$ problems. The tractable side of this dichotomy can be characterized by functions admitting quasi-polymorphisms of the ternary XOR operation, leaving open whether these cases on the $\mathrm{FP}^{\mathrm{NP}}$ side are in fact in FP. In this paper, we settle this question by giving a polynomial-time algorithm for all cases on the $\mathrm{FP}^{\mathrm{NP}}$ side. Consequently, we obtain a complete FP versus $\#\mathrm{P}$ dichotomy for counting weighted Eulerian orientations, and further for complex-valued Holant problems with an odd-arity signature. Our algorithm is based on a linear programming relaxation, but we use it in a nonstandard way. Instead of proving that the relaxation is integral and solving the problem directly from an optimal LP solution, we use the relaxation as a structural tool to lift the quasi-polymorphism condition to an ordinary polymorphism condition. This reveals an affine local structure of the constraint functions, which leads to tractability.

cs.CC↗

arXiv2025

Distributed system perspective on Backscatter systems

Backscatter system is a system based on backscatter communication technology, which is a low cost, low power consumption and easy to deploy communication technology. At present, the backscatter technology is mainly applied to RFID tags and the Internet of Things and other fields. With the rapid development of the Internet of Things, the application of backscatter systems is increasing. Moreover, the backscatter system is essentially a distributed system, but existing research rarely conducts studies and analyses from a distributed perspective. This paper conducts a study on the backscattering system from the perspective of distributed systems, comprehensively reviewing the basic principles of the backscattering system, and analyzing the distributed system architectures of different backscattering systems. Then, it introduces the application scenarios, research status and challenges of the backscattering system, and finally discusses the future research directions of the backscattering system, hoping to provide references for future research.

cs.DC↗